Macbeth avoids using the words murder or kill because he is in denial and feels guilty about his plan to kill Duncan. He is suppressing his conscience and trying to rationalize his actions by using euphemisms. This reluctance to face the reality of his plan shows that Macbeth's state of mind is conflicted and troubled.
Macbeth kills Duncan in his own castle at night time.
Macbeth believes he has to kill Duncan's guards in case they heard anything happen in the room while Macbeth was killing Duncan.
Lady Macbeth knows that Macbeth is a good man, a worthy, noble, good soldier. But she feels that he is too full of the 'milk of human kindness' (i know its meant to be a good thing, but the is the most eviliest woman in English literature we are talking about) , when it comes to killing the king. She questions his manliness, saying she is more of a man than he is. This is how she manages to convince Macbeth to kill Duncan(the king).
You'll have to rephrase this question, I'm afraid. Macbeth doesn't require Duncan to do anything. Duncan is the king, remember.
She causes it. He would never have murdered Duncan if she hadn't pushed him to it.
Macbeth is King Duncan's cousin as well as a general of the king. Later into the play, he becomes king.
Lady Macbeth talked Macbeth into killing his cousin, King Duncan of Scotland, who was a guest in his house at the time.
Duncan shows his affection for the Macbeths by giving them gifts. In particular he gives Lady M a jewel.
And then Macbeth asked Macbeth if he confronted Macbeth on killing Macbeth with Macbeth.
The king
Lady M is all for it but Macbeth is unsure and has to be pushed into doing it. He then immediately regrets it.
Lady Macbeth isn't anxious to have Duncan at Dunsinane. Dunsinane is the palatial residence where the Macbeths live after they are crowned King and Queen of the Scots. King Duncan is killed at the previous residence of the Macbeths, at Inverness. And the murder of the King is exactly why the Lady seeks, and then delights in, his presence in her home [Act 2 Scenes 5-7].