When Hamlet thinks he stabs Claudius, he gets Polonius in the arm, and makes a miraculous recovery. Since Polonius is not dead, Ophelia never goes mad.
He's going to kill Hamlet. He must be sent to jail.
When Ophelia was in the tree the branch broke and she fell into the water. Luckily someone was nearby and heard the fall. He helped her out of the water. She passed out, but soon woke up and was normal.
When Hamlet is banished to England, Rosencrantz and Guildenstern read the note that Claudius gives them, even though they were instructed not to. They disagree with the note and turn the ship around.
I now pronounce you husband and wife!
Before the battle, Gertrude sees Claudius pour the poison into what is supposed to be Hamlet's drink. Gertrude has the former king arrested and banish. He is sentenced to life in jail.
The two do not duel. Laertes speaks to Hamlet and apologizes because he did not know that it was not going to be a fair fight. They make up and become friends.
Polonius talks to Gertrude and decide to set up Ophelia and Hamlet in an arranged marriage. Hamlet becomes king and they eventually have kids together.