What role or roles does questioning and uncertainty play in Hamlet?
Questioning is definitely a major theme within this play. Hamlet himself spends most of the play questioning - should he live or die, should he believe the ghost or not, should he avenge his father's death or not. In addition, the other characters spend a large amount of time questioning - Gertrude, Claudius, and Polonius all question the reasons behind Hamlet's mad antics; Ophelia questions Hamlet's affections for her (as well as why he's acting so insanely).
Hamlet is most definitely an intellectual play, but by that I don't mean one has to be supremely intellectual or intelligent to understand it. I simply mean that its main character is a thinker, rather than a doer, and he gets stuck sometimes, running thoughts around in his head when he probably would have been better off just doing something.