"Where are the doors and windows?" is more natural English.
Is the 2nd "az" required in Hungarian, or is it optional, as it is in English?
It may not be required but I would say it is probably more common to add the second "az".
Yes. You are right.
Another case in which they need to check that the English translation is natural.
please,which would you use if the question was : where are the door and windows? van vagy vannak?