WHAT I THINK ABOUT WHEN I THINK ABOUT ACT III

Act III has definitely been the most exciting Act so far, but there is a lot that I'm unsure about. The most memorable scene is when Claudius runs out of the theater during the play where a nephew kills his uncle, the queen, and takes his place, also marrying his wife. This scene leaves a lot of questions though, mostly because of the run-through of the play before the actual play where the same plot is performed, and when Claudius doesn't react, but when it becomes evident the NEPHEW is the killer, he runs away. Also, Hamlet and his mother don't seem too concerned that Hamlet accidentally kills Polonius which makes me wonder if I misunderstood or if he wasn't really too important to him.