How do I get the currently displayed fragment?

When you add the fragment in your transaction you should use a tag.

fragTrans.replace(android.R.id.content, myFragment, "MY_FRAGMENT");

…and later if you want to check if the fragment is visible:

MyFragment myFragment = (MyFragment)getSupportFragmentManager().findFragmentByTag("MY_FRAGMENT");
if (myFragment != null && myFragment.isVisible()) {
   // add your code here
}

See also http://developer.android.com/reference/android/app/Fragment.html