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Is this the correct way to have different values/styles for different versions

Android Studio 2.1 preview 3
This is just a question, as I am confused as I have seen many alternatives in doing this.
I have created a new android project and my Activity extends AppCompatActivity
public class MainActivity extends AppCompatActivity {
I want to have the transparent statusbar on devices running 21 and over.
So in my values/styles I have the following
<resources>
<!-- Base application theme. -->
<style name="AppTheme" parent="Theme.AppCompat.Light.NoActionBar">
<!-- Customize your theme here. -->
<item name="colorPrimary">#color/colorPrimary</item>
<item name="colorPrimaryDark">#color/colorPrimaryDark</item>
<item name="colorAccent">#color/colorAccent</item>
</style>
</resources>
And in my values-21/styles I have the following
<resources>
<style name="AppTheme" parent="Theme.AppCompat.Light.NoActionBar">
<!-- Customize your theme here. -->
<item name="colorPrimary">#color/colorPrimary</item>
<item name="colorPrimaryDark">#color/colorPrimaryDark</item>
<item name="colorAccent">#color/colorAccent</item>
<!-- Make the statusbar transparent -->
<item name="android:windowTranslucentStatus">true</item>
</style>
</resources>
My Manifest I select the theme
android:theme="#style/AppTheme"
Just some questions
Is this the correct way, or is there any better way to do this?
Would values-21/styles inherit all the colors in values/styles so I would have to repeat this?

It's the right way. May I suggest you to organize your style better?
values/styles.xml
<resources>
<!-- Base application theme. -->
<style name="AppTheme" parent="CommonTheme">
</style>
<style name="CommonTheme" parent="Theme.AppCompat.Light.NoActionBar">
<item name="colorPrimary">#color/colorPrimary</item>
<item name="colorPrimaryDark">#color/colorPrimaryDark</item>
<item name="colorAccent">#color/colorAccent</item>
</style>
</resources>
values-v21/styles.xml
<resources>
<!-- Base application theme. -->
<style name="AppTheme" parent="CommonTheme">
<!-- All customization of the theme for this version -->
<item name="android:windowTranslucentStatus">true</item>
</style>
</resources>
So you don't need to repeat the common values of the style for every api level.

I will try to answer it giving some references
Maintaining Compatibility
To avoid duplication of code, define your styles inside res/values/,
modify the styles in res/values-v21/ for the new APIs, and use style
inheritance, defining base styles in res/values/ and inheriting from
those in res/values-v21/
So you should try to avoid code duplication in your style.xml at different folders res/values/ and res/values-v21/ by using style inheritance.
Style Inheritence
If you want to inherit from styles that you've defined yourself, you
do not have to use the parent attribute. Instead, just prefix the name
of the style you want to inherit to the name of your new style,
separated by a period.
If you want to inherit a style that you've defined yourself you can skip adding a parent attribute and inherit from it using a dot or period notation.
With this, you can define a base theme BaseTheme in res/values/ with different colors and inherit from it as BaseTheme.StyledStatusBar without specifying a parent attribute.
<resources>
<style name="BaseTheme.StyledStatusBar"></style>
<!-- Base application theme. -->
<style name="BaseTheme" parent="Theme.AppCompat.Light.NoActionBar">
<item name="colorPrimary">#color/colorPrimary</item>
<item name="colorPrimaryDark">#color/colorPrimaryDark</item>
<item name="colorAccent">#color/colorAccent</item>
</style>
</resources>
In values-21/, add item android:windowTranslucentStatus to BaseTheme.StyledStatusBar
<resources>
<style name="BaseTheme.StyledStatusBar">
<item name="android:windowTranslucentStatus">true</item>
</style>
</resources>
In manifest, select the theme
android:theme="#style/BaseTheme.StyledStatusBar"

1) Is this the correct way, or is there any better way to do this?
Yes. That's the correct/recommended way of having different values for different API versions.
2) Would values21/styles inherit all the colors in values/styles so I would have to repeat this?
I'm not sure I fully follow this question. Both styles you showed will inherit from Theme.AppCompat.Light.NoActionBar so your colors should be declared again, but I'll present two better alternatives:
Alternative 1, a little bit better:
Use a BaseTheme that is common for both. To view the code for it, please check #mimmo-grottoli answer.
Alternative 2, much better:
If the only different on the two themes is the android:windowTranslucentStatus that was introduced in KitKat (API level 19), you can put it all in the same theme in values/styles, like the following:
<resources>
<style name="AppTheme" parent="Theme.AppCompat.Light.NoActionBar">
<!-- Customize your theme here. -->
<item name="colorPrimary">#color/colorPrimary</item>
<item name="colorPrimaryDark">#color/colorPrimaryDark</item>
<item name="colorAccent">#color/colorAccent</item>
<!-- Make the statusbar transparent -->
<item name="android:windowTranslucentStatus">true</item>
</style>
</resources>
The Android Framework ignores XML parameters that it does not recognize. That means that on JellyBean or ICS, the device will ignore windowTranslucentStatus while correctly applying the colors and in KitKat and up, it will correctly apply windowTranslucentStatus.
That tricky is valid for all XML in Android (even layouts), the IDE might give you warnings about API level, but in XML they're always safe to use.

Different folders of values/styles are made to give a unique style when your app is running on a specific version of Android.
So yes you are right when saying that the newer version inherits from the older one. When adding items in your latest version of styles you keep the latest version up to date to the latest APIs.
To conclude, your way is the very commun way, it's an organized and a clean way to keep your app updated.

Is this the correct way, or is there any better way to do this?
Yes. That's the right way of having different values for different API versions.
Would values-21/styles inherit all the colors in values/styles so I would have to repeat this?
Yes

technically <item name="android:windowTranslucentStatus">true</item> won't give you fully transparent statusbar.
If you want it to by fully transparent, you can use <item name="android:statusBarColor">#android:color/transparent</item>

Android TimePickerDialog styling guide/docs?

I'm trying to style a TimePickerDialog for sdk 21+ (Lollipop). So far I've figured out how to change the default colorscheme in XML:
<style name="TimePickerTheme" parent="#style/Theme.AppCompat.Light.Dialog">
<item name="colorPrimary">#ff2d6073</item> <!-- no effect -->
<item name="colorPrimaryDark">#ff2d6073</item> <!-- no effect -->
<item name="colorAccent">#ff2d6073</item>
<item name="android:textColor">#ffD0D102</item>
<item name="android:textColorPrimary">#ffD0D102</item>
</style>
This works but I'm looking for a guide or documentation for all the properties I can change.
AccentColor does the basic color scheme
TextColorPrimary does the text color
But what property, for example, do I need to change the big text in the 'header' of the dialog (where the current selected time is displayed)?
Is there some documentation that lists all the possible things you can change?

After digging through the AOSP theme and style xml files and a lot of googling I made some progress. I am now able to style most(!) things.
So this is a partial answer, not all the way there yet. But here's how far I got:
You can see that I'm now able to theme the header, the un(!)selected time part (minutes in this case), the circle, the numbers in that circle and the 'hand' (or selector). Oh, and the buttons are styled, too.
Let me explain how I got things working, first: the important thing is that you can't override things directly from you app's theme OR from a (alert)dialog theme/style. You have to go from one to the next, so to speak.
Example:
AndroidManifest.xml: Set custom theme for app and/or activity
<activity>
android:theme="#style/Theme.MyTheme"
</activity>
values-v21/styles.xml: (where your custom theme resides): set the timePickerDialogTheme
<style name="Theme.MyTheme" parent="#style/Theme.AppCompat.Light">
<item name="android:timePickerDialogTheme">#style/TimePickerDialogTheme</item>
</style>
Then below that, define the timePickerDialogTheme and set the timePickerStyle:
<style name="TimePickerDialogTheme" parent="#style/Theme.AppCompat.Light.Dialog">
<item name="colorAccent">#ff2d6073</item> <!-- colorAccent here seems to work just fine? -->
<item name="android:timePickerStyle">#style/TimePickerDialogStyle</item>
</style>
Now you can define most of the styling here..
<style name="TimePickerDialogStyle" parent="#android:style/Widget.Material.Light.TimePicker">
<item name="colorAccent">#ff2d6073</item> <!-- colorAccent here seems to work just fine? -->
<item name="android:timePickerMode">clock</item>
<item name="android:headerBackground">#ff2d6073</item>
<item name="android:headerTimeTextAppearance">#style/TextAppearance.TimePickerDialogStyle.TimeLabel</item> <!-- TimePicker Time *TextAppearance* -->
<item name="android:numbersTextColor">#ff000000</item>
<item name="android:numbersSelectorColor">#ff2d6073</item>
<item name="android:numbersBackgroundColor">#ffdddddd</item>
</style>
The important line in the above is:
<item name="android:headerTimeTextAppearance">#style/TextAppearance.TimePickerDialogStyle.TimeLabel</item>
Because if you want to style the text (well, time, actually) in the header you need to define the headerTimeTextAppearance:
<style name="TextAppearance.TimePickerDialogStyle.TimeLabel" parent="#android:style/TextAppearance.Material">
<item name="android:textSize">60sp</item> <!-- from -->
<item name="android:textColor">#ffD0D102</item>
</style>
Now, if you take a look at the Widget.Material.TimePicker in AOSP styles.xml (ctrl-f 'timepicker' until you find it) you'll notice a bunch of other properties that you should be able to modify:
headerTimeTextAppearance
headerAmPmTextAppearance
headerSelectedTextColor
headerBackground
numbersTextColor
numbersBackgroundColor
amPmTextColor
amPmBackgroundColor
amPmSelectedBackgroundColor
numbersSelectorColor
Most of these work (as long as you prepend 'android:' for each of them) BUT I could not get 'headerSelectedTextColor' to work. I got a compile error saying something like "could not match property bla bla". Also, if you look at my example above, I hardcoded the textSize for the 'headerTimeTextAppearance' property because the '#dimen/timepicker_ampm_label_size' value threw errors.
In short: most of the things are listed above and how to get them working. But not all is clear. So I'd still see that complete documentation/guide :)

Android TimePicker material style with custom colors below, you can see http://www.zoftino.com/android-timepicker-example for TimePicker usage and styles.
<style name="MyAppThemeFour" parent="Theme.AppCompat.Light">
<item name="android:timePickerDialogTheme">#style/MyTimePickerDialogStyle</item>
</style>
<style name="MyTimePickerDialogStyle" parent="#style/ThemeOverlay.AppCompat.Dialog.Alert">
<item name="showTitle">false</item>
<item name="colorControlActivated">#ffd600</item>
<item name="colorAccent">#b71c1c</item>
<item name="android:textColorPrimary">#43a047</item>
<item name="android:textColorSecondary">#f44336</item>
</style>

When using version 1.5.0 of the Material Design Library for Android, I've found that I can get most of the theming with using this particular style:
<?xml version="1.0" encoding="utf-8"?>
<resources>
<style name="MyTimePickerTheme" parent="ThemeOverlay.MaterialComponents.TimePicker">
<item name="android:textColor">#FF121212</item>
<item name="android:textColorPrimary">#FF121212</item>
<item name="android:textColorSecondary">#FFF9F9F9</item>
<item name="colorAccent">#FF121212</item>
<item name="colorControlNormal">#FF121212</item>
<item name="colorPrimary">#FF121212</item>
<item name="colorSurface">#FFF9F9F9</item>
</style>
</resources>
This will yield in a generic - non colored - Dialog which works for white theme. For dark theme, simply invert the colors.
I've also asked here to have dynamic theming supported for this component.
Example screenshot using the above style:

Can't understand how to style Android app for pre-Lollipop devices using Theme.AppCompat

My brain is about to blow on Android's themes and styles. Somebody, help me, please!
I'm trying to create a theme for my app to provide as similar look for pre- and post-Lollipop devices as possible. So, I've inherited my theme from Theme.AppCompat.NoActionBar and my activities from AppCompatActivity ans set up colorPrimary, colorPrimaryDark and colorAccent. All that went well. The problems started when I tried to style background and text color. I've set android:textColorPrimary and android:textColorSecondary and got what I wanted on Lollipop device, but not on KitKat, so I've added textColorPrimary and textColorSecondary attributes to theme and after that Android Studio said that it can't build the app because these attributes can't be found. Same happened when I've tried to add colorBackground. I've tried to google it but wasn't able to found something useful about what attributes are provided by which theme and what should I use in my situation.

You must have to create two values folder one for lollipop values-v21 and simple values for pre-lollipop
See this style for pre-lollipop devices just paste it to values/styles.xml
Styles.xml
<resources>
<style name="MyMaterialTheme" parent="MyMaterialTheme.Base">
</style>
<style name="MyMaterialTheme.TransparentActivity">
<item name="android:windowBackground">#android:color/transparent</item>
<item name="android:windowIsTranslucent">true</item>
</style>
<style name="MyMaterialTheme.Base" parent="Theme.AppCompat.Light.NoActionBar">
<item name="android:windowNoTitle">true</item>
<item name="windowActionBar">false</item>
<item name="colorPrimary">#color/colorPrimary</item>
<item name="colorPrimaryDark">#color/colorPrimaryDark</item>
<item name="colorAccent">#color/colorAccent</item>
<item name="android:textColorPrimary">#color/textColorPrimary</item>
<item name="android:windowBackground">#color/windowBackground</item>
</style>
</resources>
see official documentation on android blog

If you want to style the app for different apis, you have to make a folder name values-v(sdk version) for e.g values-v21 for lollipop, values-v19 for kitkat,... but in this case I think you only need to create values-v21.
inside that folder, create an xml file style.xml and based on the api to use the appropriate attributes.

Styling the popup menu in Android 5.0

I'm making my app ready for Android 5.0, I'm using the latest compatibility library, here is what my style looks like.
<resources>
<style name="AppTheme" parent="Theme.AppCompat.Light.DarkActionBar">
<item name="colorPrimary">#color/theme_accent</item>
<item name="colorAccent">#color/theme_accent_secondary</item>
</style>
<style name="AppThemeDark" parent="Theme.AppCompat">
<item name="colorPrimary">#color/theme_accent</item>
<item name="colorAccent">#color/theme_accent_secondary</item>
</style>
</resources>
(The ActionBar color is being set programmatically.)
Now, I want the overflow/popup menu to have the dark background like it had in the holo implementation, but I can't get it to work, here is what it looks like:
I have tried setting the popupMenuStyle but it didn't work.
How can I make the popup menu darker?

Stop using the ActionBar. If you want a ToolBar to be set up like an ActionBar, follow this guide on the android-developers blog.
It actually mentions your use case at Dark Action Bar and provides this code:
<android.support.v7.widget.Toolbar
android:layout_height=”wrap_content”
android:layout_width=”match_parent”
android:minHeight=”#dimen/triple_height_toolbar”
app:theme="#style/ThemeOverlay.AppCompat.Dark.ActionBar"
app:popupTheme="#style/ThemeOverlay.AppCompat.Light" />

Not a full answer but what I found so far:
In past versions you needed to specify a drawable (Check https://github.com/StylingAndroid/StylingActionBar code and tutorials)
Apparently, now that is a color. To modify it you need to do specify the following theme:
<resources xmlns:android="http://schemas.android.com/apk/res/android">
<style name="AppTheme" parent="android:Theme.Material.Light.DarkActionBar">
<item name="android:actionBarPopupTheme">#style/popupNew</item>
</style>
<style name="popupNew" parent="android:ThemeOverlay.Material.Light">
<item name="android:colorBackground">#color/red</item>
</style>
</resources>
This works correctly if the theme applied to the app is just this.
If I add android:actionBarPopupTheme to my existing theme, it doesn't work. I am trying to figure out why.

Solved my problem by using this style:
<style name="AppTheme" parent="Theme.AppCompat.Light.DarkActionBar">
<item name="colorPrimary">#color/theme_accent</item>
<item name="colorAccent">#color/theme_accent_secondary</item>
<item name="actionBarStyle">#style/AbStyle</item>
<item name="actionModeBackground">#color/actionmode_bg</item>
</style>
<style name="AbStyle" parent="Widget.AppCompat.Toolbar">
<item name="elevation">2dp</item>
<item name="displayOptions">homeAsUp|showTitle</item>
<!--showHome-->
</style>
<style name="AppThemeDark" parent="Theme.AppCompat">
<item name="colorAccent">#color/theme_accent_secondary</item>
<item name="actionBarStyle">#style/AbStyle</item>
</style>
I had to use Widget.AppCompat.Toolbar as the parent actionBarStyle

Add the property popupTheme to your toolbar:
<android.support.v7.widget.Toolbar
xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
android:id="#+id/toolbar"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:background="#color/color_primary"
app:theme="#style/Theme.AppCompat.Light"
app:popupTheme="#style/Theme.AppCompat" />
Or define a new style for your toolbar:
<style name="MyToolBarStyle" parent="Widget.AppCompat.Toolbar">
<item name="android:background">#color/green</item>
<item name="popupTheme">#style/Theme.AppCompat.Light</item>
<item name="theme">#style/Theme.AppCompat</item>
</style>

This question has already been answered for styling via XML, but I'm adding an explanation here of how to work out the solution to this and similar styling questions yourself.
First, this is the solution when using AppCompat. To your App's style.xml add actionBarPopupTheme to your theme:
<style name="Theme.MyTheme" parent="#style/Base.Theme.AppCompat.Light.DarkActionBar">
...other stuff here
<item name="actionBarPopupTheme">#style/Theme.MyTheme.ActionBarPopupTheme</item>
</style>
<style name="Theme.MyTheme.ActionBarPopupTheme" parent="#style/ThemeOverlay.AppCompat.Light">
<item name="android:textColor">#android:color/white</item>
<item name="android:background">#android:color/black</item>
</style>
Here's the steps I took to arrive at this solution (it takes a bit of detective work as the Android documentation is poor):
Open your App's style.xml in Android Studio
On the line where you App's theme is defined, put your screen cursor in the parent theme (e.g. click in #style/Base.Theme.AppCompat.Light.DarkActionBar) then press F4. This should take you to the source code for the style in the appcompat library.
Within this style I saw this line:
< item name="actionBarPopupTheme">#style/ThemeOverlay.AppCompat.Light< /item>
This looked like a possible place to change the theme of the popup. I searched for "actionBarPopupTheme" in the poor
Android developers documentation and found "Reference to a theme that should be used to
inflate popups shown by widgets in the action bar". So this was worth playing with.
I copied the appcompat line containing "actionBarPopupTheme" to my style.xml then in this line replaced the item's theme reference (the bit in bold above) with Theme.MyTheme.ActionBarPopupTheme.
In my style.xml I created my new style named Theme.MyTheme.ActionBarPopupTheme. I used the same parent that was used in the style I copied from the appcompat source (the bit in bold above).
To ensure my new popup style was working, I changed the parent style to ThemeOverlay.AppCompat.Dark then ran and tested the code on a device. The popup style changed, so now I knew my overriding of actionBarPopupTheme was the correct thing to do. Then I changed back to ThemeOverlay.AppCompat.Light.
The next challenge is to work out what item names to override in Theme.MyTheme.ActionBarPopupTheme. I changed the text and background colours. To find the correct item names that change the style of something can be tricky in some cases. One way to find less obvious style item names is to look through the style definitions in the appcompat xml file (the one you opened when pressing F4 in the 2nd step above), continually descending into parent styles (F4 again!) until you find something that may do what you want. Google searches will help here too.

Change the line color used in listSeparatorTextViewStyle

I have the following code
<TextView
android:text="#string/hello"
style="?android:attr/listSeparatorTextViewStyle" />
and I will get the following effect.
However, I am not happy with the color line. I would like to have something like
I would like it to have blue color line as in holo. I try the following custom style.
<style name="MyOwnListSeperatorTextViewStyle">
<item name="android:background">#android:drawable/list_section_divider_holo_light</item>
<item name="android:textAllCaps">true</item>
<!-- Copy from Widget.TextView.ListSeparator -->
<item name="android:background">#android:drawable/dark_header_dither</item>
<item name="android:layout_width">match_parent</item>
<item name="android:layout_height">wrap_content</item>
<item name="android:textStyle">bold</item>
<item name="android:textColor">?textColorSecondary</item>
<item name="android:textSize">14sp</item>
<item name="android:gravity">center_vertical</item>
<item name="android:paddingLeft">8dip</item>
</style>
But it won't work, as I get the following error.
error: Error: Resource is not public. (at 'android:background' with value '#android:drawable/dark_header_dither').
Have idea how can I change the line color used in listSeparatorTextViewStyle?

I needed to do this to override the typical Holo Spinner style (I didn't want the underlined item - i just wanted the arrow), and I think this can be overridden in precisely the same manner:
First off, you want to find the item you wish to override in the android styles source. There is an incredibly useful SO answer that contains all of the styles (and the names to override them) right here: Set Dialog theme to parent Theme in Android
I believe yours is the following line:
<item name="listSeparatorTextViewStyle">#android:style/Widget.Holo.Light.TextView.ListSeparator</item>
This takes us on a journey to find the style Widget.Holo.Light.TextView.ListSeparator which should live somewhere on your very own computer! But I'll make it easy and just c&p it:
<style name="Widget.Holo.Light.TextView.ListSeparator" parent="Widget.TextView.ListSeparator">
<item name="android:background">#android:drawable/list_section_divider_holo_light</item>
</style>
Now, you probably want to leave well enough alone, and just look at that background drawable. You will find it is a grey 9patch file that looks like the sinister grey line you seek to avoid.
We need to override this. I am sure there are a number of ways to do this, but I do so by customizing the theme of the application. Here is the themes.xml file:
<style name="AppTheme" parent="#android:style/Theme.Holo.Light.NoActionBar">
<item name="android:listSeparatorTextViewStyle">#style/MyOwnListSeperatorTextViewStyle</item>
</style>
<style name="MyOwnListSeperatorTextViewStyle" parent="Widget.TextView.ListSeparator">
<item name="android:background">#drawable/make_your_own_blue_9_patch_here</item>
</style>
Notice how we used the listSeparatorTextViewStyle from that previous SO post? And the parent of the custom style is the Widget.TextView.ListSeparator from android's style source? All very important.
Now you just need to apply this theme to your app, but I am assuming you have a theme already. If you haven't already, you will need to make your own 9patch but I would just look at the list_section_divider_holo_light.9.png file on your computer, and make the grey parts blue, and then make a copy and place it into your own drawables folder.
Hope this works and is helpful!