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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>

Repeating style in v19/v21

I have this in my styles.xml:
<style name="UserTheme" parent="ThemeBase">
<item name="android:editTextStyle">#style/EditTextTheme</item>
</style>
Why do I have to repeat the editTextStyle line in v19/styles.xml and v21/styles.xml.
v21/styles.xml:
<style name="UserTheme" parent="ThemeBase">
<item name="android:windowTranslucentStatus">true</item>
<item name="android:windowTranslucentNavigation">true</item>
<item name="android:editTextStyle">#style/EditTextTheme</item>
</style>
Is there a way to just call it in the main styles.xml and have it apply everywhere so I don't have to write it multiple times?

I couldn't find any recommended solution so I i digged into AppCompat source. The way they do it is like this.
In your styles.xml
<style name="Base.V7.Theme.YourThemeName" parent="Theme.AppCompat.Light.NoActionBar">
</style>
<style name="Base.Theme.YourThemeName" parent="Base.V7.Theme.YourThemeName" />
<style name="Theme.YourThemeName" parent="Base.Theme.YourThemeName" >
<item name="colorPrimary">#color/primary</item>
<item name="colorPrimaryDark">#color/primary_dark</item>
<item name="colorAccent">#color/accent</item>
</style>
In your styles-v21.xml
<style name="Base.V21.Theme.YourThemeName" parent="Base.V7.Theme.YourThemeName">
<item name="android:navigationBarColor">#color/white</item>
<item name="android:windowTranslucentStatus">true</item>
</style>
<style name="Base.Theme.YourThemeName" parent="Base.V21.Theme.YourThemeName" />
In your styles-v22.xml
<style name="Base.V22.Theme.YourThemeName" parent="Base.V21.Theme.YourThemeName">
<item name="android:navigationBarColor">#color/black</item>
<item name="android:windowTranslucentStatus">false</item>
</style>
<style name="Base.Theme.YourThemeName" parent="Base.V22.Theme.YourThemeName" />
For every new version you extend the previous base version. If you want to override any attribute for different version just put it inside Base.VXX.Theme.YourThemeName block on your new styles-vXX.xml file.

Why do I have to repeat the editTextStyle line in v19/styles.xml and
v21/styles.xml?
If you've applied some STYLE to some attribute, Android will search styles.xml file for highest api level for which file_api_level<=Android_device_api_level and searches for STYLE in it. If it finds it would apply that STYLE to view otherwise will continue searching for the STYLE in lower api level files.
e.g. - If you have four files styles.xml(default), v19/styles.xml, v21/styles.xml, v25/styles.xml and your devices is running on api level 24. Then it'll search for STYLE in v21/styles.xml first, then v19/styles.xml and finally in styles.xml(default). Only first occurrence of the STYLE will get applied. So you can't just define only extra attributes in version-specific styles.xml file.
If you don't want to repeat common attributes here is an alternate. To declare window transitions for Android 5.0 (API level 21) and higher, you need to use some new attributes. So your base theme in res/values/styles.xml could look like this:
<resources>
<!-- base set of styles that apply to all versions -->
<style name="BaseAppTheme" parent="Theme.AppCompat.Light.DarkActionBar">
<item name="colorPrimary">#color/primaryColor</item>
<item name="colorPrimaryDark">#color/primaryTextColor</item>
<item name="colorAccent">#color/secondaryColor</item>
</style>
<!-- declare the theme name that's actually applied in the manifest file -->
<style name="AppTheme" parent="BaseAppTheme" />
</resources>
Then add the version-specific styles in res/values-v21/styles.xml as follows:
<resources>
<!-- extend the base theme to add styles available only with API level 21+ -->
<style name="AppTheme" parent="BaseAppTheme">
<item name="android:windowActivityTransitions">true</item>
<item name="android:windowEnterTransition">#android:transition/slide_right</item>
<item name="android:windowExitTransition">#android:transition/slide_left</item>
</style>
Now you can apply AppTheme in your manifest file and the system selects the styles available for each system version.
Is there a way to just call it in the main styles.xml and have it
apply everywhere so I don't have to write it multiple times?
Yes, there is a way in which you can maintain only one styles.xml file.
First of all, start using AppCompat themes. They provide backward compatibility and will work for older android versions as well.
Now define all of your styles in styles.xml(default) file and if your Android Studio is showing you some warning/error for some attribute which is supported in higher level apis:
You can suppress that warning using: tools:targetApi="SupportedAndroidVersionName"
Now Android will ignore that particular attribute if it's not supported and your whole style will work perfectly for both lower and higher api levels.
Read more about Styles and Themes here.
Hope it helps :)

Newer versions of Android have additional themes available to applications, and you might want to use these while running on those platforms while still being compatible with older versions. You can accomplish this through a custom theme that uses resource selection to switch between different parent themes, based on the platform version.
Why do I have to repeat the editTextStyle line in v19/styles.xml and
v21/styles.xml?
Because if your app is running on v21, v21/styles.xml will be loaded and if running on v19, v19/styles.xml will be loaded. In case you don't have v21/styles.xml or v19/styles.xml the app will automatically use your default values/styles.xml but you wont be able to take advantage of new features provide only for v21 or v19.
For more reference you can read Supporting Different Devices and Select a theme based on platform version.

Android: java.lang.IllegalStateException: You need to use a Theme.AppCompat theme (or descendant) with this activity

I still got a crash report because of this Exception
java.lang.IllegalStateException: You need to use a Theme.AppCompat theme (or descendant) with this activity.
I have searched about it, still can't figure it out how to fix this.
I have using Theme.AppCompat.Light as base AppTheme. Here my style.xml
<!-- Base application theme. -->
<style name="AppTheme" parent="Theme.AppCompat.Light">
<!-- Customize your theme here. -->
<item name="colorPrimary">#color/toolbar</item>
<item name="colorPrimaryDark">#color/toolbar_dark</item>
<item name="colorAccent">#color/accent</item>
<item name="android:windowNoTitle">true</item>
<item name="windowActionBar">false</item>
<item name="drawerArrowStyle">#style/DrawerArrowStyle</item>
<item name="android:windowContentOverlay">#null</item>
<item name="actionOverflowButtonStyle">#style/OverFlow</item>
<item name="searchViewStyle">#style/ActionBarSearchView</item>
<item name="colorControlActivated">#color/switch_activated</item>
<item name="colorSwitchThumbNormal">#color/switch_normal</item>
<item name="android:colorForeground">#color/switch_track</item>
</style>
I only have 1 style.xml inside values folder
I'm using crashlytics in my app, I got this problem only from some device, but this is really annoys me.
Is there anyone know hot to fix this?
I have done both of things below, but still got a crash report.

You are getting this problem because you have derived one or more of your Activity classes from ActionBarActivity. You need to either derive from Activity OR you need to use one of the Theme.Appcompat styles for your ActionBar. And make sure you specify the correct android:theme attribute in all your <activity ... /> declarations in your manifest.
EDIT:
Add android:theme="#style/AppTheme" to the declaration of MainActivity in your app manifest. And change parent="Theme.AppCompat.Light" to parent="#style/Theme.AppCompat.Light" in res/theme.xml.

Android 5.0 is not supporting for lower versions

Please help me.
I got struck in solving this error for more than 3 days
I didnot get the proper solution.
I have updated my eclipse to run android 5.0.
I had created a simple android application using minimum version 16 and target version 21 to run android 5.0 material theme.
Have added the theme in styles.xml as like this
<resources>
<!-- inherit from the material theme -->
<style name="AppTheme" parent="android:Theme.Material">
<!-- Main theme colors -->
<!-- your app branding color for the app bar -->
<item name="android:colorPrimary">#color/primary</item>
<!-- darker variant for the status bar and contextual app bars -->
<item name="android:colorPrimaryDark">#color/primary_dark</item>
<!-- theme UI controls like checkboxes and text fields -->
<item name="android:colorAccent">#color/accent</item>
</style>
</resources>
I followed the link to add supporting libraries appcompatv7.
http://developer.android.com/tools/support-library/features.html#v7
But I am getting error stating that R cannot be resolved to variable
whenever I add this appcompat to my project.
please give me a suggestions and also please share your android 5.0 running in lower version project.

for api lower than 21 use Theme.AppCompat instead of android:Theme.Material
please read here http://developer.android.com/training/material/compatibility.html

Your theme.xml should be something like this.
<?xml version="1.0" encoding="utf-8"?>
<resources>
<style name="AppTheme" parent="AppTheme.Base"/>
<style name="AppTheme.Base" parent="Theme.AppCompat.Light.NoActionBar">
<item name="colorPrimary">#color/grey_main</item>
<item name="colorPrimaryDark">#color/grey_main</item>
<item name="android:windowNoTitle">true</item>
<item name="windowActionBar">false</item>
</style>
</resources>

check your mainactivity.java.
your r.java file could have not generated so that you might get error mentioning R cannot be Resolved
Must add Add appcompat into your project library
sdk\extras\android\compatibility\v7\appcompat
Add AppBaseTheme
<style name="AppBaseTheme" parent="Theme.AppCompat">

read compatibility for material theme and add appcompat into your project as library that you can find in
sdk\extras\android\compatibility\v7\appcompat
than
your style.xml
<style name="AppBaseTheme" parent="Theme.AppCompat">

How to change action bar background when using the Support Library?

I tried example code (https://developer.android.com/training/basics/actionbar/styling.html) on 'Customize the Background'.
but I want to know how this works. -> '#drawable/actionbar_background'
It seems to add 'actionbar_background.png' file to somewhere res folder but I don't know where.
So I changed source like this.
<!-- Action Bar styles -->
<style
name="MyActionBar"
parent="#style/Widget.AppCompat.Light.ActionBar.Solid.Inverse">
<item name="android:background">#FF6600</item>
<!-- Support library compatibility -->
<item name="background">#FF6600</item>
</style>
but this part
<item name="background">#FF6600</item>
doesn't work.
I don't know what type is appropriate.

Please Use this in style.xml in res>>Values
<resources>
<!--
Base application theme, dependent on API level. This theme is replaced
by AppBaseTheme from res/values-vXX/styles.xml on newer devices.
-->
<style name="AppBaseTheme" parent="android:Theme.Light">
<!--
Theme customizations available in newer API levels can go in
res/values-vXX/styles.xml, while customizations related to
backward-compatibility can go here.
-->
</style>
<!-- Application theme. -->
<style name="AppTheme" parent="#android:style/Theme.Holo.Light">
<item name="android:actionBarStyle">#style/MyActionBar</item>
</style>
<style name="MyActionBar" parent="#android:style/Widget.Holo.Light.ActionBar">
<item name="android:background">#4cb9f6</item>
</style>

In my case I also couldn't change the background using the XML style file, so I just changed the color inside the "onCreate" of my activity.
getActionBar().setBackgroundDrawable(new ColorDrawable(Color.parseColor(MY_COLOR)));
Maybe this isn't the best practice, but it is functional.