I really have no answers to these questions, but wondered what people thought about them and if there's anything in the text to give us a hint to any answers.

Did Polonius know Claudius killed King Hamlet? He seems to be Claudius' right hand man, was he in on the plot? And if not, does he ever suss it out? At the play, perhaps?

He is Claudius' man, but was he King Hamlet's? Was he Chamberlain under the former king or did he advance to that position when Claudius came into power?