Why does he not kill Claudius when he sees him in Act III, scene iii?
Hamlet decided not to kill Claudius because Ā he believes that Claudius' soul will go to heaven. Hamlet knew his father didn't had the chance to repent of his sins so sending Claudiu's to heaven wouldn't be a fair revenge for him.
Why does he kill Polonius in Act III, scene iv?
Hamlet believed that Claudius was behind the arras and stabbed him with a sword. Unfortunately, Polonius was the spy.
How do these two actions affect your understanding of Hamlet as a man of thought or a man of action?
Hamlet made mistaken choices. He obsessed by existencial questions like if it is worth living, if he should commit suicide or kill his uncle. He was a man of though and action in my opinion. Trying to revenge his father committed a lot of mistakes which makes me think he got mad not knowing what to really do.
