To what degree does Claudius believe Hamlet is a threat to him?

Claudius sees Hamlet as a huge threat. The reason I think this is because of King Cladius's behavior regarding Hamlet. In Act 2 Scene 2 when King Claudius was confronted with matters of foreign affairs and instead wanted to know the reasons for Hamlet's behavior, it causes the reader to wonder about King Claudius's priorities. King Claudius is a selfish man, and does not worry about the well being of others, but instead focus's on the well being of himself and furthering his personal desires. Because of King Claudius's extreme distraction with Hamlet's erratic behavior and obsession with the cause of it, it leads me to believe that King Claudius knows Hamlet is up to something, and considers him a great threat to everything he has recently gained.

Does Hamlet really love Ophelia?

In my mind, Hamlet did not love Ophelia. For the most part the reason I think this is based on Hamlet's encouter with Ophelia in Act 2 Scene 1. Shakespeare did not even give us the firsthand account of the interaction, instead the reader was told through Ophelia's conversation with her father Polonius. For this reason, i think Hamlet's odd behavior toward Ophelia was because he knew Ohpelia would tell her father, and it could help further his case of madness. Hamlet also knew that after Ophelia told polonius about the encounter, the first thing he would do was go to King Claudius. To really understand this, you have to think about Hamlet's motivations, what he is untimatly trying to do throughout the play, and take that into consideration when judging his actions.