Short answer: what are there to think about is wrong; what's on hers is right.

When what is used substantively, that is, as a noun, as opposed to an adjective, it can only be singular and have a singular verb if it is the subject. In what's there to think about, it is used substantively, so you can't replace is with are. You would have to turn it into an adjective to do so:

What things are there to think about?

Here what functions like an adjective modifying the (substantive) noun things.

What can refer to something vague, like "everything on her answer sheet": when you use what, you don't always need to refer back to a specific word. In your clause what's on hers instead, the vague reference is perfectly fine. What are would not be correct.