Answer to Question 1: Hamlet becomes increasingly furious with both himself and whoever harmed those who he cared about. A visceral sentiment of vengeance consumes him as he realizes his mind won't be at peace if he simply stands around fearfully inside his aristocratic eggshell, and the sentiment won't snuff out until the ones responsible for his anger are punished.
Answer to Question 2: Hamlet believes he will become a beast if he gives himself into an avenging wrath, but it does not matter to him as long as his grieving thoughts are cleansed. Ignoring the incident would simply preserve his plight.
Answer to Question 3: The audience should feel compasion for the man in duel, and be afraid that a good man who's well aware of his own thoughts and conclusions - a man that has lost nearly everything - gave into the rage.
Director's notes on Proper Soliloquies.
An actor who aims to perform a soliloquy must look around their environment, focus on a significant element of the scene, and procced to describe with detail how the sight makes them feel - repeat the process with the rest of the scene -. The actor should change the tone of their voice between the lines depending on the current feeling of their character; shouting it all should not be neccesary and might be considered exaggerated.
