Is it strictly "love" in this case or should "Who does this girl like?" be accepted as well?
I translated as "Is this the girl whom you like?".
How would I ask on this way then? :)
No. We don't use the -ing form with "love" in natural English -- it's a stative verb.
So we say "I think you are right" and "I love you" and "I have a book in my pocket" and "I don't understand" -- not "I am thinking you are right" or "I am loving you" or "I am having a book in my pocket" or "I am not understanding".
actually...i believe you are being wrong here....you can definitely say "I am thinking you are right" or "I am loving you" or "I am having a book in my pocket" or "I am not understanding". as well as "who is she loving"...in english there is a division between "to do" something and "to be doing" something....similar to "i've ben loving you a long time" you can say "i am loving you"... to put it bluntly, -ing is just stating that something is not happening in that particular moment. Lets say there is a difference between loving someone and being in love with someone. In any case, my main question is actually, is there such a division in Hungarian (play/playing, love/loving, drive/driving etc.) or not?