Does Claudius think Hamlet is crazy?

I think Claudius' main reason for sending Hamlet away is that he is afraid Hamlet knows what he did and is not actually crazy, just mad with vengeance. That is why he is so curious as to why Hamlet is crazy and why he sends so many people to spy on Hamlet or try to pry it out of him. Very early in the novel, I think in act 1, Claudius tells Hamlet that he wants him to stay in Denmark. That seemed weird to me at first, but looking back I think Claudius just wanted Hamlet to stay around so he could keep an eye on Hamlet. If Hamlet went away and found out what happened, he could sneak back and kill him. With Hamlet nearby he can have someone always keep watch on him. I think Claudius does not think Hamlet is crazy and that scares him.

2 Questions...

1 - Based on Hamlet's response to Ophelia, does he know that Polonius is listening to their conversation?

2 - Why does Hamlet call Ophelia a whore when she has not done anything that we know of to deserve it?

Does He love Ophelia?

To be honest. I can't really tell. I think if he really did though, he might tell her what he is doing or something. He might have told her not to worry and that he will be back, but he didn't. This leads me to believe that maybe he never really cared for her. I think that he might have liked her a little, but his primary motivation in wanting to be with her was exactly what Polonius was worried about - that all Hamlet wanted was a little action. It doesn't really say it, and there is no hard evidence, but judging by the way he treats her just before (and slightly after he goes crazy) and the crude jokes and comments he makes towards her, I feel like Hamlet's interest in Ophelia was primarily physical.

Act 3

Act 3 - The Development of Hamlet

Hamlet, to me, appears to not be crazy. This act makes me believe that Hamlet is actually incredibly cunning. He seems to be able to turn on and off his craziness, which makes me believe it is just an act. His response to Ophelia and his advice to her that all women are liars and that they should only marry foolish men shows another side of him that I did not really see before. I thought he was only depressed and possibly crazy, but now I think he has changed from depressed to angry and violent. The way he stabs blindly into the curtain shows his rage against Claudius is insanely strong, because he stabbed someone behind a curtain when he thought it was Claudius. However, his rage is not enough to overtake his wit, because his plot to reveal the king through the play is genius. Hamlet was developed from a depressed, crazed man into a vengeful, angry, shrewd man in this act.