Macbeth

She tries to wipe imaginary blood off her hands and she relives killing Duncan and Banquo.

"From this moment, the very firstlings of my heart shall be the firstlings of my hand." In other words, the first thing he thinks of doing will be the first thing he does. Or in different other words, he will act solely on impulse, without any consideration.

He will get kings though he be none.

The question is about Act 3 Scene 6. It's a curious scene because the conversation is very guarded and non-specific. However, there can be no doubt that Lennox has correctly deduced that Macbeth is guilty of the murders of Duncan and Banquo and the suspicion on their sons is a smokescreen. The other Lord calls Macbeth a "tyrant" which is considerably more plain.

Duncan, about the first Thane of Cawdor. Of course, his next choice for Thane of Cawdor is someone else in whom he builds an absolute trust, namely Macbeth. Truly, Duncan is useless at finding the mind's construction in the face, which might make him a saint or an idiot, but in any event a man unequipped to be an effective king.

Well, if by this you mean how do we know that Macbeth killed Duncan, his line in Act 2 Scene 2 "I have done the deed" is pretty clear. If you mean does he feel guilty about doing it, how about "This is a sorry sight" which he says while looking at his bloody hand shortly after.

It's difficult to say. One possibility is that the ghost was fulfilling Banquo's promise to "fail not the feast" and so he sits in the only available place. Or possibly, he wants to sit in the place which will be sure to get Macbeth's attention. Or he is trying to twist Macbeth's tail by reminding him of the witches' prophecy by sitting in the king's seat, except that the prophecy said his children would be kings not him.

Macbeth, after being told that he's to be made Thane of Cawdor, says "Two truths are told, As happy prologues to the swelling act Of the imperial theme." Remember that the witches in 1,3 hailed him as Thane of Glamis, Thane of Cawdor and King of Scotland hereafter. He already knew at the time that he was Thane of Glamis and now he finds that he was Cawdor as well! Two true statements! and leading up to the most interesting, most important theme or topic of all, the one having to do with kingship. OK, "monarchic theme" would have been more accurate strictly speaking, since there is nothing about his being an emperor (imperial means having to do with empires and emperors), but accuracy was not W. Shakespeare's middle name.

they observe how lady macbeth rubbs her hands constantly and her mental actions/behavior

Real witches, who cursed the play because Shakespeare used real incantations in the verse

Marry in lent, you will learn to repent.

Well, a play on the subject of Macbeth was famously written by William Shakespeare in around 1605. A number of movies have been made based on this play or on a plot similar in some way to it.

Shakespeare was a man and Anne was a woman. Coincidentally the same applies to Macbeth and Lady Macbeth.

England

Just about nobody is loyal to Macbeth at the end. Seyton (sounds like Satan and who knows? it might be him) is one of the last to stay with Macbeth.

Macduff

You need to specify. There are a number of scenes between Banquo and Macbeth.

In Act 1 they are living in Inverness, possibly in a castle or possibly in a large house. By Act 5 they are living at Dunsinane, which is a castle.

O, full of scorpions is my mind, dear wife

scorpions refers to superstitions and doubts. and to some extent. it can mean horrors.

hope that helped!

He chopped it off with a sword, then put it on a spike, or stick, then showed it to the cheering crowed

Although the people of that era believed in witches, the witches in Macbeth were very probably not portrayed as frightening. The very silly scenes involving songs and the headwitch Hecate (which were likely not written by Shakespeare, but were written also in the Jacobean Era) make the witches sillier than the fairies in Midsummer Night's Dream, and although these scenes are never played nowadays, there is every reason to think that this was actually how the witches were played at first. This may have been the only way to get them onstage in a time when people would have been genuinely frightened of representations of real witches.

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Macbeth's first reaction is to dismiss the prophecies out of hand, as would any sane person. However, the grain of truth, and his own ambition, are what lead him to wonder, though not necessarily believe, the prophecies to be true. It can be argued that it is not his reaction to the prophecies which is important, but that of his wife. Lady Macbeth, who does not hesitate to believe the prophecies, is the one to spur her husband into the actions that follow, and lead to his eventual downfall.

TO make sure that it was carried through. Some even think that the third murderer was Macbeth

As in England calling your son the Prince of Wales marks him as the heir apparent, Duncan's calling Malcolm the Prince of Cumberland marked him as the next king. This would certainly be "a step on which [Macbeth] must fall down, or else o'erleap."