What questions should I ask?

It might help you greatly, if you address the expectations of the parents. What do they expect their child to learn, any specific experiences they want them to have. The question of family dynamic is one that should be broached a little indirectly; if head-on, it will often result in answers that don't totally paint the correct picture of what is truly going on in a home. College studies that I've had show that if a person is asked confronting questions, they will often evade and that won't help you at all. Break your questions down into a conversational fact-finding mode. A lot can be learned from indirect queries.