(Scene 1, Lines 1-45) As the king, it is Claudius's duty to see that justice is
done for the murder of Polonius. Does he set the wheels of justice in
motion? How does his handling of this crime affect his image with the
audience?

there are number of topics. you can pick any one of these topics:

the author motivation is to show the power of animal-human relationships.

reading poetry is challenging when you don't have or very little of social context and culture schema.

solution: read the introduction, the norm, or even explaination if you still dont get it.

are you kidding? from that description of two mansions, you can't figure out which one is bleak and desolate? maybe you should consider looking those words up in a dictionary, if you don't know what they mean already.