"I go to the second floor, and you?"
Translation:A második emeletre megyek, és ti?
That should be accepted, I agree. "En" is not necessary but you can emphasize the fact that it's you who does this so it should be accepted. Same in Italian and many other languages.
Exactly! This is a great example of continuous tense - this is exactly when we need it. Happening right in the moment as I am standing in the elevator and asking: "I'm going to the second floor, and you?" Yes, "you" means "Te, Ti, On, Onok" is. None of those were reflected in the answer.
Or a második emeletre járok in Hungarian (I habitually visit the second floor).
Not unless it's emphasized like in the a.m. example. Most of the time we don't say "I" just like in Italian.