"You are" is not the same as "your"
The verb should agree with the subject, and when the subject is "you" the verb (to be) becomes "are"
However in your example, the question
What is your problem?
Is formed from the statement:
Your problem is ...
The subject here is "Your problem" and that is singular. The word "Your" acts to modify the word problem, but it doesn't change it to plural. The verb agrees with the singular "problem" *"What are your problem" is absolutely wrong.
However if you have "problems" you would use "are"
Your problems are ...
What are your problems?
Exactly the same rule applies to "homework" which is singular.