How to get a Fragment to remove itself, i.e. its equivalent of finish()?

You should let the Activity deal with adding and removing Fragments, as CommonsWare says, use a listener. Here is an example:

public class MyActivity extends FragmentActivity implements SuicidalFragmentListener {

    // onCreate etc

    @Override
    public void onFragmentSuicide(String tag) {
        // Check tag if you do this with more than one fragmen, then:
        getSupportFragmentManager().popBackStack();
    }
}

public interface SuicidalFragmentListener {
    void onFragmentSuicide(String tag);
}

public class MyFragment extends Fragment {

    // onCreateView etc

    @Override
    public void onAttach(Activity activity) {
        super.onAttach(activity);
        try {
           suicideListener = (SuicidalFragmentListener) activity;
        } catch (ClassCastException e) {
           throw new RuntimeException(getActivity().getClass().getSimpleName() + " must implement the suicide listener to use this fragment", e);
        }
    }

    @Override
    public void onActivityCreated(Bundle savedInstanceState) {
        super.onActivityCreated(savedInstanceState);
        // Attach the close listener to whatever action on the fragment you want
        addSuicideTouchListener();
    }

    private void addSuicideTouchListener() {
        getView().setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View v) {
              suicideListener.onFragmentSuicide(getTag());
            }
        });
    }
}

What I don't understand is what to do in Df when 'OK' is pressed in order to remove fragments Df, Cf, and Bf?

Step #1: Have Df tell D "yo! we got the OK click!" via calling a method, either on the activity itself, or on an interface instance supplied by the activity.

Step #2: Have D remove the fragments via FragmentManager.

The hosting activity (D) is the one that knows what other fragments are in the activity (vs. being in other activities). Hence, in-fragment events that might affect the fragment mix should be propagated to the activity, which will make the appropriate orchestration moves.

You can use the approach below, it works fine:

getActivity().getSupportFragmentManager().popBackStack();

While it might not be the best approach the closest equivalent I can think of that works is this with the support/compatibility library

getActivity().getSupportFragmentManager().beginTransaction().remove(this).commit();

or

getActivity().getFragmentManager().beginTransaction().remove(this).commit();

otherwise.

In addition you can use the backstack and pop it. However keep in mind that the fragment might not be on the backstack (depending on the fragmenttransaction that got it there..) or it might not be the last one that got onto the stack so popping the stack could remove the wrong one...