About his Situation and Actions:
* Why did you feign madness? Was it a genuine act, or did you ever truly lose your mind?
* How did you feel about your father's death? Did you love him? How did his murder affect you?
* Why didn't you kill Claudius right away? What were your internal conflicts and reservations?
* What was your relationship with Ophelia like? Did you truly love her?
* Do you regret your actions against Polonius, Ophelia, and Rosencrantz and Guildenstern?
* Did you ever truly forgive yourself for your inaction and the consequences that followed?
About his Thoughts and Beliefs:
* What is the purpose of life? What is your view on death and the afterlife?
* Do you believe in revenge? Is it ever justified?
* How do you reconcile your desire for justice with your sense of morality?
* Do you believe in fate? Or do we have free will to make our own choices?
* What is your understanding of human nature? Are people inherently good or bad?
* What role does doubt play in your life? Do you ever question your own sanity?
About the Play and the World:
* What do you think about the court of Elsinore? How does it compare to the world outside?
* Do you believe in the power of words? Can they change the course of events?
* What is the role of the individual in a society like this?
* What are your thoughts on the nature of power and ambition?
* What do you think is the ultimate message of your story?
More Personal Questions:
* What is your favorite book? Your favorite play?
* What is your favorite pastime?
* What are your dreams and aspirations?
* What are your biggest fears?
* What is your greatest regret?
Remember, these are just starting points. Depending on the context and your approach, you can ask Hamlet a variety of questions to probe his character, his experiences, and his inner world.