Which one is correct:  ''You gave it to whom? or  To whom did you give it?''?

The "whom" is the indirect object (object of a preposition) in each situation.  The difference lies solely in whether you desire to create a question by verb inversion, or by intonation.  The difference between Do you like it, and You like it?

Almost every English speaker in the world would say "Who did you give it to?" Those who listen to made-up rules that have nothing to do with how English is spoken would say "To whom do you give it?" which sounds so awkward most listeners would assume they were joking. "You gave it to whom?" or, in real life, "You gave it to who?" or even "You gave it to him?" would be said with a rising inflection on the last word to indicate that you find it hard to believe what the other person just told you.