Hamlet

He asks her not to go to Claudius' bed.

Queen Gertrude.

"The best way out is always through" means that if you keep going through what you're already going through (presumably a negative experience) you will eventually come out the other side...and it will be over.

^To add to this, the presumption is also (seeing as it is the 'best' way out) that among any other options -- like avoidance -- it is best to just engage/deal with whatever the problem or hardship is rather than to give up or look for a way around the problem. Possibly this notion comes from the idea that if you deal with the problem directly, it is forever solved and therefore can't come back around to bite you in the posterior.

yes he is related to luis

Claudius shows respect towards Polonius. Since Polonius is the advisor to the King, kind of like the second in command, Claudius could only have treated him with respect.

Laertes didn't have any "important realisations" during his duel with Hamlet. The duel only took place as a means for Claudius to have Hamlet killed, disguised as Laertes' need to seek satisfaction for the deaths of his father and sister.

Laertes had forgiven Hamlet, but needed to uphold his reputation and honour, hence the duel.

Claudius hopes that Hamlet will be killed in England. Claudius is the King and is also the brother of Hamlet.

He is talking about his mother. He switches to talking about Claudius in the next line.

Polonius

Revenge Tragedy is a technique used in plays. It involves the leading character avenging the death of a loved one. The most famous Revenge Tragedy is William Shakespeare's 'Hamlet'.

The only protagonist in Hamlet is Hamlet, who emerges victorious only in the sense that he does end up getting his revenge on Claudius. Everyone else dies in the process, however.

In a sense, they do not care about the outcome of the duel. The duel is a smokescreen to give Laertes an opportunity to be within arm's length of Hamlet with a pointy poisoned sword, and with some kind of excuse when Hamlet is killed as a result. Hamlet was, in fact, winning the duel and would have won the bet for Claudius, but that doesn't matter.

What Polonius says might seem like practical and wise advice. His closing exhortation, "to thy own self be true" is often sententiously quoted. The significance of this fatherly advice is that when we find out, in Act 2 Scene 1, that Polonius is sending a spy to check up on Laertes by slandering him about the town, we realize that Polonius himself is not to himself true and he is, as we increasingly find out, false to every man. He doesn't expect Laertes to listen to his wise advice, because he wouldn't think of following it himself. He is just putting on a show.

Purgatory.

Well, the ghost tells him in Act 1 Scene 5 to "Revenge my most unnatural murder" and Hamlet doesn't do it until Act 5, after about three hours of play. But Hamlet is not really a procrastinator. He really only has one good chance at killing the king and passes on it because he thinks he will get a better chance. When he thinks that better chance has come, he doesn't hesitate: he stabs the man hiding in the curtains, who turns out to be not the king at all. Basically the ball he left alone turned out to be a strike and the one he swung on he should have left alone.

Killing a king is not an easy thing to plan out. You need to wait for an opportunity and take it when it comes, or you will be yet another in the long list of failed assassins. If Hamlet had rushed down from the battlements and broken into the place where the king was taking his rouse, waving a sword and attempting to stick it in Claudius in some hypothetical Act 1 Scene 6, the actor playing Hamlet would not have had to worry about learning any lines for the rest of the play. Hamlet would have been dead meat.

flowers, herbs, ans straw

Hamlet tells Ophelia to get to a nunnery. However, "nunnery" not only meant convent but was also slang for whorehouse. It's a matter of interpretation every time he says it which one he means, or whether he might mean both.

He is in his late 20s

2 months

The uncle poured poison down his father's ear.

Hamlet suspects that Claudius, his uncle, is a murderer in that he suspects that Claudius killed Hamlet's father, Claudius's brother, in order to become King.

When the Ghost reveals to Hamlet that he was killed by Claudius, Hamlet's immediate reaction is, "O my prophetic soul! My uncle?"--which is a pretty clear indication that Hamlet had some serious suspicions beforehand.

no

Ophelia is directed by her father in Act 1 Scene 3 to forget about Hamlet because he is too far above her socially. She therefore acts as if she no longer cares about him, as she confirms "as you did command I did repel his letters and deny his access to me." Later when she and Hamlet meet she returns his lovetokens "I have remembrances, Lord which I have longed long to redeliver". But she is all too aware that Polonius is just behind the nearest arras and she is saying this for his benefit, not Hamlet's.

After Hamlet has berated her by telling her to "Get thee to a nunnery!" her speech, "O what a noble mind is here o'erthrown" shows that she still cares deeply for Hamlet.

Unfortunately in the world of the subtle games Hamlet is forced to play, Ophelia is way out of her depth. It's appropriate that she drowns.

"Denmark's a prison."

Avenge his murder

Not Denmark. Horatio is unfamiliar with the customs in Denmark: when Claudius first starts his trumpet and cannon accompaniment to his drinking, Horatio asks "Is't the custom?" whereupon Hamlet replies that it is but "to my mind though I am native here and to the manor born, it is a custom more honoured in the breach than the observance." If Horatio had been Danish he would have known that this was a custom.

Horatio and Hamlet met at University in Germany: Horatio may be German.