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In which situation we want to add fragment without container?

Fragment transaction has method add(Fragment fragment, String tag), which does not place fragment to container, so it cannot have view. For what it can be used?

From the Android Documentation:
However, a fragment is not required to be a part of the activity layout; you may also use a fragment without its own UI as an invisible worker for the activity.
How about this purpose ?
Simple example: an Activity starts an AsyncTask, but when device rotated activity restarts, causing AsyncTask to lose connection with the UI Thread. But this Activity can hold a Fragment (invisible, with no UI at all) that can handle all the AsyncTask work. When Activity recreated the Android OS takes care reattaching the Fragment, thus no data loss will occur.

For Dialogs you don't have any container on normal app layer. It is directly added on Window with WindowManager(See WindowManager.LayoutParams for various types of layers).
DialogFragment has an API like DialogFragment.html#show(android.app.FragmentManager, java.lang.String) which corresponds to this.

You can use fragments without UI (container) as a background worker (one benefit is that you can retain it during rotations etc) and for retaining data during rotations and other changes.
Reading http://developer.android.com/guide/components/fragments.html is strongly recommended.
Example of instance retaining: https://android.googlesource.com/platform/development/+/master/samples/ApiDemos/src/com/example/android/apis/app/FragmentRetainInstance.java
Also, here are similar questions (so this questions seems to be a duplicated but cannot be flagged due to bounty):
What is the use case for a Fragment with no UI?
Android non-UI Fragment usage

As #Lucius Hipan mentions, it can be used to prevent data loss.
Almost always this king of fragments are used as Retained container ( setRetainInstance(true) called in onCreate method), then after device configuration changes (e.g. orientation changing) fragment will not be recreated but remembers previous state.
It's recommended way to use asynctask.
Here is an example:
There is login activity. The user enters their credentials and presses the Login button. After that configuration change occurs (user rotates phone). So, network task was completed, but your handlers was not listening for it now. If you show any login animation, it can be stored via savedInstance, but listeners not. And instead of creating service you can simply create new retained fragment with persistant asynctask and interface to communicate with activity.
This method is a good compromise for small projects where using bus libraries is overstatement.

By calling the method add(Fragment fragment, String tag) internally calls add(int containerId, Fragment fragment, String tag) with a 0 containerId.That will be add(0, fragment, tag).
If 0 is supplied as containerId, it will not be placed the fragment in a container.

When (& where) are my fragments created

I'm using the viewpagerindicator library (http://viewpagerindicator.com/) to create some sort of wizard for my android app. It works fine and does exactly what I want.
I would like to "extend" the functionality a bit by having "previous"/"next" buttons in my ActionBar - pretty much as in Android's "Done Bar" tutorial - to step through the wizard. Works like a charm, too.
HOWEVER:
I would like to display information about the "next" & "previous" fragment in the ActionBar's buttons. Information I pass to the fragments that live in the ViewPager at the time of their "creation" (actually at the time of their object instantiation - using the classical "newInstance(...)" approach to create the instance of my fragment, store the parameters in a Bundle and extract them in the fragment's "onCreate" method). The same way the template does it, when you create a new fragment for your project.
So, this information is the thing I actually want to display in my wizards button to know what fragment is next and which was last.
The type of this information is not important for my problem. It could be a String or an icon or an int or ... anything else you want.
However, wherever I've tried to access my fragments data, the fragment has not yet been fully initialized (meaning its "onCreate" method has not been called yet).
I've tried it in the host fragment's "onViewCreated" method, because I thought that's where all its subviews should be initialized already (at least their "onCreate" method should have been called, I thought), but it seems that this is handled differently for ViewPager to retain only the number of fragments in memory that was set by setOffscreenPageLimit.
So, what I'm looking for (and probably just missing) is the correct callback method here. One that is called when the ViewPager's next Fragments have been loaded and initialized. If such a callback exists, I could place my little piece of code there to update the text in my "previous"/"next" buttons within the ActionBar.
Any help, comments, ideas are highly appreciated. If needed, I can also try to attach some code sample to better explain my setup, but I think it should be easy enough to understand what my problem is.
Thanks in advance!
P.S.: I also tried to do this by using EventBus to send "onFragmentInitialized" messages from my fragments within in the ViewPager and the hosting fragment. It actually worked, but it does not seems the proper way to do this.

When a Fragment's onCreate Method is called, its already preparing to be displayed, and practically its past the point where its considered a Next or Previous fragment instead its considered current.
A fragment's onCreateViews method is called after committing a transaction in the FragmentManager. which takes less than 1 sec to bring it in front of the user (depending on the device and runtime environment)
But in your case, your data should be initalized outside the Fragment that uses it, and displayed where ever you want by passing the data itself then displaying whatever you want form it.
decouple your data from android objects (Fragment, Activity ...) and you should be able to load, maintain, access it cleanly and without worrying about their callbacks.

The Fragment's arguments can be read and loaded in its onAttach callback rather than onCreate, the Activity will then (after onAttach is complete) get a onAttachFragment callback with the Fragment as a parameter. However, I doubt onAttachFragment will be called when switching between already loaded pages in the view pager.
If not, you could have the fragment notify the activity (through an interface) that it is now active during its onActivityCreated, onViewCreated or similar method.
But it sounds more like the activity should register as a page changed listener to the ViewPager itself, and update its state depending on the page rather than which fragment is active.
As a side note, ViewPagerIndicator is quite old now (hasn't been updated in 3 years), a more modern approach is the SlidingTabs example from Google, which has been built into a library available here: https://github.com/nispok/slidingtabs

Fragment doesn't refresh

I have a Fragment that shows some data saved in android Preference.
when these data changes due to various operations of the app, I want to update the fragment with the new data.
I have tried to use
myFragmentTransaction.notifyAll();
But unfortunately doesn't work and the fragment is updated only when I reopen my whole Activity
Houw could I refresh the Fragment on data changes?

notifyAll pertains to threading. Completely unrelated to what you are doing. Instead of trying to tell each fragment to redraw themselves have you tried OnSharedPreferenceChangeListener. Each fragment should listen to changes in the information they care for.

Android login and forgot password - Actvity or fragment

I am creating a login page which will have forgot password right now:
Login Page is one Activity and Forgot Password page is another Activity.
Each one calls an AsyncTask for http post which returns a json response.
Hence I have callback listener in each `Activity.
In the call back listener I get the json response, which I parse in separate Activity for each Login and separate one for Forgot password
I need to know whether its good practice to do this way or use fragments. Also any other better way to developing it?

I would suggest using a Fragment per page, so one for "Login" and one for "Forgot Password", and one Activity that handles the async http request. You would then be able to use the fragment methods such as fragment.replace() to swap out the screens without each fragment having to have a callback listener. The activity then can also parse the callback listener once instead of twice in each separate activity. Also, the way Android is heading, Fragments are better to use for UI elements than separate Activities as it makes UI updates quicker and smoother then starting a new activity.
There is an Android Developer API Guide loaders available to every Activity and Fragment. Why not check it out. On that same site you can also find guides to use fragments in your activity.

Asynctask in Fragment or Parent Activity?

I have a scenario and I an not sure on what path to go.
Scenario
The app has a Home activity which displays various fragments. The data in the fragments can come either from the web or a local database and is retrieved using an asynctask.
From what I saw, I have 2 alternatives:
Put the Asynctask in parent activity and then use fragment.newInstance(parameters) to pass the result to the fragment. However, if in my asynctask I need to update the progress or some info on the fragment, each time I will have to call newInstance with the new set of parameters.
Add the fragment and put the asynctask in it, in this way when progress is needed, I can update the fragment's views, as I have access to them + when the asynctask is done, I can populate the list with the info.
What would be the correct approach ?
LE: actually for point 1 in order to update the fragment I can call fragment's public methods after I find it with findFragmentById in the parent activity

A better way if you have multiple tasks would be to use an IntentService :
http://mobile.tutsplus.com/tutorials/android/android-fundamentals-intentservice-basics/
You would have a better control to what you're requesting and what you want to cancel.

I would go with the second approach.
My primary reason though would be to avoid the issues that can happen on screen orientation change while the AsyncTask is working.

I would go with method 2, but take it a step further.
Have a separate fragment to run your async task. This way, you can handle any configuration changes (not just rotating screen) without any issues.
In another fragment, you can display the data. You can pass the data from your async task fragment via callbacks to the activity, and have the activity call a method in the display fragment to update the data.