Macbeth sees the ghost of the recently murdered Banquo.
No, Lady Macbeth is not aware that Macbeth has planned the death of Banquo and Fleance.
Macbeth kills him because Banquo starts to work out that Macbeth killed dDuncan
You need to specify. There are a number of scenes between Banquo and Macbeth.
The ghost of Banquo.
*Banquo. Macbeth's best friend is Banquo, but he is also Macbeth's enemy. After the meeting with the witches, Macbeth finds out that he will become the Thane of Cawdor and the King of Scotland. Eventually, he achieves both of these prophecies. Banquo, Macbeth, and Lady Macbeth are the only people that know about the witches. Banquo becomes suspicious of Macbeth because Macbeth fulfills the prophecy after King Duncan is murdered, and Macbeth acknowledges this fact. Basically, Macbeth doesn't trust Banquo.
Macbeth kills Banquo in the play and then Banquo's ghost haunts Macbeth.
Macbeth's best friend was Banquo. They fought together in battle before Macbeth's rise to power.
Macbeth kills Banquo in the play and then Banquo's ghost haunts Macbeth.
Macbeth sees the ghost of the recently murdered Banquo.
No, Lady Macbeth is not aware that Macbeth has planned the death of Banquo and Fleance.
Macbeth's soldiers do not kill Banquo, Macbeth hires three murderers to do the job.
Macbeth kills him because Banquo starts to work out that Macbeth killed dDuncan
In Act 3 of Macbeth, Macbeth becomes suspicious that Banquo poses a threat to his throne. He worries that Banquo's descendants will inherit the crown, as the witches prophesied. This suspicion leads Macbeth to plot Banquo's murder.
It is not known who kills Banquo but it is Macbeth who orders for him to be murdered.
She doesn't. She says, "How did you dare to trade and traffic with Macbeth in riddles and affairs of death, and I the mistress of your charms, was never call'd to bear my part or show the glory of our art?" In other words she's cheesed off that the other witches went ahead without giving her a piece of the action. She doesn't care about Macbeth or Banquo one way or the other.
In both cases, the ghost that appears in Macbeth is summoned by the guilt and inner turmoil of Macbeth himself. The ghost of Banquo is a manifestation of Macbeth's guilt over his role in Banquo's murder, while the ghost of Lady Macbeth represents his guilt over her death and his descent into madness.