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We cannot answer that. We know that Claudius was in love with her before King Hamlet's death because he lists "his queen" as one of the motives of the murder. Whether she reciprocated we cannot say.
People who expect the monarchy to pass by primogeniture (as the English monarchy does and did in Shakespeare's day) would expect Prince Hamlet to have been the heir to King Hamlet. Thus it is ironic for Claudius to say that Hamlet is most immediate to Claudius's throne because by the rules of primogeniture, Claudius has usurped and Claudius should be the most immediate to Hamlet's throne. There is a further irony in that in fact in Denmark at the time, the rules of primogeniture did not apply and Claudius would indeed have been the rightful heir, especially having married the widow of the previous king, but the audience, thinking they know better, would consider him to be a usurper.
Claudius denies Hamlet from heading back to Wittenberg. It should be noted that Hamlet made the choice himself, but was persuaded by Claudius to say no.
When Gertrude inadvertently drinks the poison and dies, Hamlet is at last able to bring himself to kill Claudius, and the king is felled by his own cowardly machination. Addition: Act 5, Scene II: "HAMLET The point!--envenom'd too! Then, venom, to thy work. Stabs KING CLAUDIUS All Treason! treason! KING CLAUDIUS O, yet defend me, friends; I am but hurt. HAMLET Here, thou incestuous, murderous, damned Dane, Drink off this potion. Is thy union here? Follow my mother. KING CLAUDIUS dies"
Claudius and Gertrude
Hamlet changes the letter going to the King of England to kill him when he gets there to say to kill the people who give you this letter,which were Rosencrantz and Guildenstern. So they were killed instead.
The king as in the ghost? he tells him to get revenge on Hamlet Sr. (the ghost) brother, Claudius because he was the one who killed him. He also told him not to hurt his mother for marrying Claudius because Hamlet Sr. made her that way and she didn't know that Claudius killed him.
Well, I must first of all say that my statement is of my own interpretation of the story. However, it may be possible that Claudius was planning on killing off Hamlet (or at least spy on him) from the very beginning. By looking at Claudius's personality, namely his willingness to kill for power, it can be implied that Claudius is fearful of loosing his power in the same way. Of all that may pose a threat to Claudius, Hamlet seems to be the most likely threat as he is in direct line to the throne (after all why not kill off the king and become the new king a little ahead of schedule?). So due to Claudius's paranoid nature, it may be possible that he intended to keep Hamlet in Elsinore so that he could plot to get rid of him.
Claudius advises Hamlet to stop mourning his father's death and start celebrating the marriage between him and Hamlet's mother. He calls Hamlet's attitude"stubborn and unmanly." A little insensitive considering Hamlet's father has only been dead for 2 months at the time.
Hamlet doesn't actually stage a play called The Mousetrap. He asks the travelling players (The Tragedians of the City) to put on The Murder of Gonzago, which is the real name of the play. Hamlet calls it the Mousetrap because his purpose in asking them to play it is to trap Claudius into a confession of guilt.
To take Hamlet to England to be killed, Claudius can't have Hamlet killed in Denmark because it would upset Queen Gertrude along with many others who still praise him even though he seems to have lost his mind. However on the trip to England Hamlet changes out the letters to say kill these men---Rosencrantz and Guildenstern. The priates of the ship are told that they will be paid well if they send Hamlet back. And they believe him due to his charming personality and style of clothing which is not commender fashioned. Rosencrantz and Guildenstern are sent to the King of England and take the punishment of what was supposed to be Hamlet's death.
Because he believes that because King Claudius is praying, he soul will be cleansed. Because of this, he would not be damned to hell or purgatory when he dies. Instead, Hamlet decides to wait until King Claudius has slept with the Queen later that night before killing him (theoretically his soul would be sullied because of this). The reason this is such a big deal is because the ghost of old King Hamlet wanders trapped in purgatory since he didn't have a chance to confess his sins.