Hamlet Reading

There were a couple of things that stood out to me in the first act of Hamlet! For starters Hamlet is denied his return to France by his uncle, something that still makes no sense to me... Secondly, the king wants the prince and country to get over the loss of their former king Hamlet. I understand that he killed him but why does he fear being caught so much if he is oblivious to the fact that Hamlet senior's spirit is roaming the castle. Thirdly, why does Horatio ask Hamlet not to follow the ghost if he himself asked him to speak to it! I am very excited to see what revenge Hamlet has in store towards his uncle!