Brainstorming 'Hamlet' questions for ENGL 102

I'm wondering what questions will connect with my students.

1. Had Hamlet and Ophelia already hooked up when Polonius prohibited their relationship?

2. Is Hamlet hallucinating, or has he seen a ghost (the spirit of a dead person), or is he being fooled by a demon?

3. Is Hamlet mad, faking it, upset but still basically normal, or what?

4. Why did Kate Winslet, Billy Crystal, Robin Williams, and so many others think it was worthwhile to be in Kenneth Branagh's film version of Hamlet?