这个问题需要在Fragment中处理返回键（back button）的事件。我们需要重写onBackPressed()方法，判断当前的Fragment是否是HomeFragment，如果是的话，就将App退出。如果不是，则返回HomeFragment。

同时，我们还需要处理弹出DialogFragment时的返回键。同样地，在DialogFragment中重写onBackPressed()方法，并在里面调用dismiss()方法，即可达到和点击dialog外部一样的效果。

下面是代码示例：

public class HomeFragment extends Fragment {

    // ...

    @Override
    public void onResume() {
        super.onResume();
        ((AppCompatActivity) getActivity()).getSupportActionBar()
                .setTitle(getString(R.string.home_fragment_title));
    }

    @Override
    public void onViewCreated(@NonNull View view, @Nullable Bundle savedInstanceState) {
        super.onViewCreated(view, savedInstanceState);

        view.findViewById(R.id.btn_show_dialog).setOnClickListener(v -> {
            DialogFragment dialogFragment = new MyDialogFragment();
            dialogFragment.show(getChildFragmentManager(), "MyDialogFragment");
        });
    }

    @Override
    public void onActivityCreated(@Nullable Bundle savedInstanceState) {
        super.onActivityCreated(savedInstanceState);
        setHasOptionsMenu(true);
    }

    @Override
    public void onCreateOptionsMenu(@NonNull Menu menu, @NonNull MenuInflater inflater) {
        super.onCreateOptionsMenu(menu, inflater);
        inflater.inflate(R.menu.menu_home, menu);
    }

    @Override
    public boolean onOptionsItemSelected(@NonNull MenuItem item) {
        if (item.getItemId() == R.id.action_settings) {
            NavHostFragment.findNavController(this).navigate(R.id.action_homeFragment_to_settingsFragment);
            return true;
        }
        return super.onOptionsItemSelected(item);
    }

    @Override
    public void onBackPressed() {
        if (getActivity() != null && !getActivity().isFinishing()) {
            new AlertDialog.Builder(getActivity())
                    .setTitle("Confirmation")
                    .setMessage("Are you sure you want to exit the app?")
                    .setPositiveButton(android.R.string.yes, (dialog, which) -> {
                        getActivity().finish();
                    })
                    .setNegativeButton(android.R.string.no, null)
                    .show();
        }
    }
}

public class MyDialogFragment extends DialogFragment {

    @Override
    public void onCreate(@Nullable Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setCancelable(true);
    }

    @Override
    public View onCreateView(@NonNull LayoutInflater inflater, @Nullable ViewGroup container, @Nullable Bundle savedInstanceState) {
        return inflater.inflate(R.layout.fragment_dialog, container, false);
    }

    @Override
    public void onViewCreated(@NonNull View view, @Nullable Bundle savedInstanceState) {
        super.onViewCreated(view, savedInstanceState);
        view.findViewById(R.id.btn_close_dialog).setOnClickListener(v -> {
            dismiss();
        });