Ophelia's Madness

I would say that Ophelia's madness was caused by the events leading up to her father's death. She had to reject Hamlet, who she loved but was told not to be with. Then, Hamlet began acting crazy and kills Ophelia's father. Even though what he did to Polonious was unintentional, he took the life of his ex-lover's father. The fact that it was Hamlet who killed Ophelia's father could have driven her into madness. Her madness could have been passed to her by Hamlet even though he was faking it or it was based off the tragedy of her father's death and the murderer Hamlet.

Hamlet's hesitation to kill Claudius

I agree with Hamlet's hesitation to kill Claudius. I think that if he were to carry out the deed, that he should take his time to contrive an effective plan instead of just going about it with a higher chance for mistake. If he were to get caught, his position in as a prince would be compromised. The public would completely turn against him. Murdering the king would probably result in his immediate execution (even though Claudius has planned Hamlet's death in England).