2. Yes you'd say "coming" - because you are placing yourself in position to the teacher who will also be in class; just as she would say "Are you coming to class tomorrow?"
If a friend said to you: "Are you coming to Joe's party?" it would mean he's going to it.
If he said "Are you going to Joe's party?", perhaps he isn't going, or hasn't decided yet.
So, coming and going can also refer to where you and the other person will be, as well as to where you both are now.