Act 3, 3 and 4 scene ?s

1) What does Claudius plan to do with Rosencrantz and Guildenstern and Hamlet?
To send Hamlet and his two "friends" to england to get rid of him so Hamlet wont kill him and so Hamlet can calm down and not go crazy.
2) What is Polonius going to do while Hamlet speaks with his mother?
Going to spy on them and tell Claudius about what they were talking about. 
3) List three important things about Claudius’ soliloquy.
a) He still wants what he killed his brother for
b) He commits that he killed his brother
c He wants to be innocent and free but he knows he can't 
4) Why is it odd that Hamlet sees the king praying?
Because the king still wants what he killed his brother for which made him want to pray so he can be relieved of his sins
5) Why doesn’t Hamlet take this opportunity for revenge?
Because he wanted to kill him but now he doesn't because since he admitted he would go to heaven and Hamlet doesn't want him to go to heaven.
Scene IV
1) Describe Polonius’ advice to Gertrude.
To be Hamlet's mother and give consequences that Hamlet will have to deal with. 
2) What is the significance of the following quote: “How now, a rat? Dead! For a ducat, dead!
That Polonius is a rat and he will be dead because Hamlet strike  him right after it was said
3) What is odd about the following quote: A bloody dead; almost as bad, good mother, as kill a king and marry with his brother.
Hamlet is saying what he did was bad but what his mom did was horrible when she married her old husbands brother.
4) Why might Gertrude say, “What have I done, that thou dar’st wag thy tongue in noise so rude against me.”
She wants to know why Hamlet is yelling and making fun of her the reasoning why she is being treated wrong.
5) What descriptions does Hamlet use to compare his father and his uncle?
King Hamlet
He is compared to gods in the lines 56- 63, "Hyperion's curls... did seem to set his seal." 
Claudius
He is compared to a decaying rotting piece of corn, from the lines 64- 68, "Here is your husband... Ha, have you eyes?"
6) What point does Hamlet make by comparing the men?
That Gertrude was stupid because she went from amazingness like gods to wanted a rotten decaying ear of corn. 
7) What is disturbing about the following: Nay, but to live in the rank sweat of an enseamed bed; stewed in corruption; honeying, and making love over the nasty sty.”
Its disturbing because Hamlet wants to know about his mom's sex-life when his mom is like 50 years old.
8) What stops Hamlet’s ranting and raving at Gertrude? What does this figure tell Hamlet?
Hamlet stops because he sees his father in ghost form again but Gertrude can't see it, the ghost says for Hamlet to comfort his mother and not to take revenge on her for his father's death.  
9) By the end of the act, Hamlet has made many statements about humanity, in general. Explain a few of his points. Do his opinions reflect his madness.
10) Explain the differences between the ghost in Act I with the ghost in Act III. Why might these differences reflect Hamlet’s insanity? 
Ghost in act 1 was more of a warning and more then just Hamlet saw the ghost before. In act 3 however he was the only one that saw his ghostly father's appearance