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Using getSupportFragmentManager when using AppCompatDelegate?

I'm using AppCompatPreferenceActivity, that is an Activity which extends PreferenceActivity and has an AppCompatDelegate. I want to add a headless fragment to this Activity, but I can't call to getSupportFragmentManager...
Is there a way to add fragments to a PreferenceActivity using AppCompatDelegate?

The only way to call getSupportFragmentManager is from a FragmentActivity or something which derives from it. PreferenceActivity derives from Activity which cannot use Fragments.
You should look into using a PreferenceFragment instead.

Android viewpager in fragment

Dear ladies and gents,
First of all, please do not mark my question down. If you think that my question is too stupid please let me know and i will edit it or remove.
So my actual question is that I have an activity (extends Activity). In that activity's layout I created FrameLayout where I then attach different four fragments(so each of them extends Fragment. So in one of that fragments I would like to implements swipeable tabs(see screenshot).
I know that it is usually done by implementing viewPager and FragmentPagerAdapter, but I can not do this as if I'm calling getSupportFragmentManager in my fragment it gives my an error. If i am using getActivity().getFragmentManager() it gives me error that android.support.v4.app.fragmentmanager cannot be applied to android.app.fragmentmanager. I have to use android.support.v4.app.fragment in my fragment, because otherwise I will not be able to implement my activity's view(described at the beggining).
Any ideas or suggestions would be very appreciated.screenshot

Make sure you are using Fragment class that you extends your fragments comes from support library. You also need to use FragmentActivity to call method getSupportFragmentManager();
On the other hand, viewpager which is in your fragment need to implemented as usual that you can find on internet except getChildSupportFragmentManager();
This one called "nested fragments".
PS: I am not sure but you can also use AppCompatActivity instead of FragmentActivity. FragmentActivity and ActionBarActivity must be deprecated.
Good luck

You can use getChildFragmentManager() when using Fragments inside other Fragments.

New version of Support Library v4 (Android 4.2) resolve this problem. For do this, simply do constructor of your custom FragmentPagerAdapter like this:
public CustomFragmentPagerAdapter(android.support.v4.app.Fragment fragment)
{
super(fragment.getChildFragmentManager());
// write your code here
}
This work because new Android version approve using nested Fragments

Cannot resolve method getActivity()

I am new to Android and learning to create fragments in Android by following this
example: Fragment Navigation Drawer
The code between Navigating between Menu Items and Add Navigation Header consists a method getActivity().
As the author didn't mentioned where to paste this code, I pasted in my MainActivity.java file
Is code between Navigating between Menu Items and Add Navigation Header pasted at correct location by me?
In method selectDrawerItem(MenuItem menuItem) there is a comment // Create a new fragment and specify the planet to show based on position
Does author expects me to add something over here.
The project files layout created by me on AndroidStudio is as follow:AndroidStudio Snapshot

You can use:
this Or `MainActivity.this`
Instead of:
getActivity()

An Activity has no getActivity() method.
Fragments have.
Because getActivity() says: "return the Activity which contains me".
And while Framents are contained in Activities, Activities themselves aren't.

It has been clearly pointed out that you cannot use the getActivity() method in an activity. Well, other alternatives apart from the this keyword could be;
Get current activity context : using the getContext()
This method can be called on a View like text view like so textView.getContext(); This will give the context of the activity in which the view is currently hosted in. i.e something like so View.getContext();
Get App-level context : getApplicationContext() this method returns the activity that houses the entire life cycle of the application.

In Fragment it is best to use onAttach() method to get the instance of an Activity attached to it.
here is a sample code:
#Override
public void onAttach (Activity activity) {
super.onAttach(activity);
}

How do I dynamically update a fragment in a FragmentPagerAdapter

I'm writing a simple Fragment Activity with a FragmentPagerAdapter and two Fragments, where I need to show certain data in tab2 related to my selection in tab1. But the data in tab2 is never updated. Is there any common procedure for this?

You'll need a common holder for data, Activity object is most suitable, since it is parent of both fragments. All fragments can use getActivity() in onCreate(). You can call a method of Activity object to get selected data. The other fragment can similarly, call a method of Activity object to set selected data.

Solved. I just created one instance of each Tab and added an update() method on tab 2 which I called from Tab 1. I couldn't find a built in solution so I did it my way.

Communicating between fragments in Android

Based on the example from http://developer.android.com/training/basics/fragments/communicating.html I tried to reproduce the communication between two fragments which are sub fragments of a larger fragment.
In the example, AB activity contains A fragment and B fragment. But I am trying to achieve the same but in my case AB Fragment contains A fragment and B fragment.
The problem is the overridden method in the AB Fragment never gets called. Does this not work because the containing component is a Fragment and not a Activity like in the example? Am I missing out something here?

If you are referring to onClick() or some other onSomething() handler, then these always get called in the Activity class, not the fragment. So in the example you linked, the onArticleSelected() must remain in the Activity, even if you have nested fragments.
To pass info on to the fragment, you have a few options. One, you can keep a reference to the fragment within the activity. This might be lost if your activity recreates (settings event for example).
The second and better way would be to tag your fragments, and then use findFragmentByTag.
When you add your fragment (notice the parameter "my_fragment" which is the tag I gave to the fragment):
getSupportFragmentManager().beginTransaction().add(R.id.fragment_container, myFragment, "my_fragment").commit();
Or when you replace one fragment with another:
getSupportFragmentManager().beginTransaction().replace(R.id.fragment_container, myFragment, "my_fragment").comit();
Then, when you want to do something in the fragment from within your onArticleSelected of the activity:
Fragment fragment = getSupportFragmentManger().findFragmentByTag("my_fragment");
if (fragment != null) {
fragment.articleSelected(articleId);
}

You can always use an Interface to communicate between fragments. It is the safest way to do so.