1. Both are OK.
2. Only the second works.
Interested in Language
I have an exam tomorrow.
I am having an exam tomorrow.
I think the second one is more natural.What could you say?
At a party you ask someone: Do you go home? or Are you going home?
I think both variants can be used. What could you say?
'Do you have to go home?' should also be understandable.
Not a teacher.