When he killed Polonius he thought he was killing Claudius. Everyone else he killed, he killed on purpose.
He thought he was killing Claudius.
The king was praying at the time, and Hamlet thought that by killing him at that time, the king would go to heaven.
Before Hamlet enters his mother's chamber, Polonius is having a discussion with Hamlet's mother Gertrude. As Hamlet enters the room, Polonius conceals himself behind a tapestry hanging from the wall. When he hears Gertrude begin to feel threatened by Hamlet, he cries out for help, thinking that he would kill them both. Hamlet hears Polonius, and believes him to be a rat/spy (possibly even King Claudius, but it is unclear if he truly believes this). Hamlet stabs through the tapestry killing Polonius, who remarks "O, I am slain".
The first plan for killing Hamlet which we know about is to send him to England to deliver orders to the English authorities that they should put Hamlet to death.
No, he wanted him to take revenge on Claudius for killing him when he didn't get a chance to confess his sins. Old Hamlet is angry at this because he is now in purgatory. He is also angry at the thought of Claudius sleeping with Gertrude and marrying her so soon after his death.
He is talking about Claudius and about killing him.
Since, at the time he does so, Hamlet himself is fatally poisoned, Hamlet completely wipes out the Danish royal family by killing Claudius. This creates a vacuum into which the opportunist Fortinbras steps.
Polonius didn't have any type of cover or guard while listening in on the conversation and wasn't expecting for Hamlet to notice him, "him"(What Hamlet had thought was the supposed Claudius) It was maybe because Hamlet had thought Polonius was Claudius, but even so. Polonius hid behind the tapestry or the arras while he was eavesdropping on Gertude and Hamlet. Hamlet thought that it happened to be the king Claudius who was spying on him and had hid behind there, but to his unknowing, after slashing away at the cloth he found that he had killed Polonius. Hamlet, instead of being shocked by killing the man said that he was a fool and hid his body somewhere.
No, Gertrude is lying as Hamlet suggested she should.
The consequences of Hamlet killing Polonius is that he planted the seeds of discord between the supporters.
that isn't a question
Jealousy was the driving force behind Claudius killing his brother, King Hamlet, is because he is jealous and wants to be the king so he can have more power and do whatever he plays. He gave in to temptation and did what he thought would allow him to get him what he wanted with no one to stand in the way.