What events happened act iii of hamlet?

Act 3 is a busy act in Hamlet. Rosencrantz and Guildenstern make a report to the king, and he and Polonius plan to spy on Hamlet. They place themselves in a hidden space with Ophelia as bait. Hamlet strolls along and makes his "To be or not to be" speech. He sees Ophelia and they have a very peculiar conversation which ends with Hamlet getting angry with her and accusing her of prostituting herself (figuratively). Ophelia thinks he has lost his mind ("O what a noble mind is here o'erthrown") but Claudius draws the opposite conclusion. That's Scene 1.

In Scene 2, Hamlet meets up with the players, and after telling them how to do their job, asks Horatio to watch Claudius during the play. The play is then performed with Hamlet being terrifically rude both to the actors and to his fellow audience members. Claudius spots that the play is all to similar to his murder of Hamlet Sr. and demands that it stop. As he exits, Hamlet is exultant: the Ghost has been vindicated! Rosencrantz and Guildenstern show up and tell Hamlet to visit his mother.

On the way, Hamlet spots his uncle praying. We hear part of the prayer and know that Claudius is feeling guilt for murdering his brother. Hamlet is about to kill him then hesitates, deciding to wait until Claudius is doing something sinful. Nevertheless he says he could "drink hot blood" and he is now going to give his mother a talking-to.

In Scene four, Hamlet arrives at his mother's bedroom and begins chastising her. Polonius, hiding behind a curtain, hears and echoes Gertrude's cries for help. Hamlet, believing his moment to kill Claudius has come at last, kills Polonius thinking that he is the king. He then launches into a long tirade to his weeping mother, and is only stopped by the appearance of the Ghost. Gertrude is persuaded that Claudius is a murderer and agrees to help Hamlet, and Hamlet drags the corpse of Polonius off.