What message do Rosencrantz and Guildenstern carry to the King? What is the King's response?
Hamlet doesn't really give them straight answers. The boys tell Claudius of Hamlet's interest in the theater troop. Claudius tells them to encourage Hamlet's interest in the play.
Hamlet's famous "To be or not to be" soliloquy is in the scene one. In a sentence or two paraphrase his main points:
Hamlet talks about whether it's better to live or commit suicide.

He's afraid of what happens after you're dead; it's against the Catholic religion to commit suicide and that's why people live and suffer because they are afraid of life after death.

Describe Hamlet's tone when he speaks to Ophelia:
Hamlet is angry and he tells Ophelia to become a nun and to never marry or have children. Because, he reasons, that children become people and they become terrible. Hamlet's kind of losing it.
What do the King and Polonius decide about Hamlet's condition after eavesdropping on Hamlet and Ophelia?
Claudius doesn't think Hamlet is love-crazy, he thinks that he is sad.

Polonius still thinks that he is mad and that it's caused by unrequited love for Ophelia.

Why does Hamlet give instructions to the players?
He wants them to perform a scene similar to how he thinks his father's murder was played out. He wants to watch Claudius reaction to the scene to see if he acts guilty.
What was the King's reaction to the play, and what did Hamlet and Horatio decide his reaction meant?
Claudius stops the play.

Hamlet and Horatio decide that this means the King is guilty of poisoning King Hamlet like the ghost said.

What message does Rosencrantz deliver from the Queen?
The message is that the Queen wants to talk to Hamlet before he goes to bed, she wants to have an "attitude adjust" with Hamlet.
The King has Rosencrantz and Guildenstern prepare to do what? Why?
The King wants them to go to England with Hamlet in order to protect the country from the danger of Hamlet's craziness getting out of control.
Why doesn't Hamlet kill the King when the King is kneeling?
Hamlet doesn't kill the King when he is kneeling because he is praying to repent his sins. Hamlet believes that King Hamlet didn't go to Heaven because he never repented for his sins. He wants to wait for the King to sin again before killing him so that Claudius will go to hell instead of heaven.

How does Polonius die?
Polonius dies from being stabbed. He was hiding behind a tapestry and he spooked hamlet who stabbed him without knowing who he stabbed.
What would Hamlet have his mother do?
He wants he to stop bonking the new King and to confess and repent her sings. He doesn't want her to tell King Claudius that Hamlet's craziness is an act.