What I Think About When I Think Of Act III

In act III of Hamlet, a lot of things happened. I still don't understand why Hamlet didn't kill Claudius when he had the chance, because he thought he would go to heaven for repenting of his sins. To bad after Hamlet left, Claudius said his thoughts were low and he wouldn't be able to go to heaven for them. When Hamlet killed Polonius, I saw it coming. First of all, Polonius shouldn't have been eavesdropping on a personal conversation between mother and son, and second, why would he yell from behind a curtain and not show his face? I really hoped that when Hamlet's father's ghost appeared that Gertrude would see him as Hamlet does and realize he isn't as mad as people may think.