In Act 5, why is Lady Macbeth sleepwalking? What does that suggest about her state of mind?
To answer your first question about Lady Macbeth's sleepwalking:
Sleep, or the lack of sleep, is a major motif in the play. For example, after Macbeth kills Duncan, he tells Lady Macbeth: "Methought I heard a voice cry 'Sleep no more! / Macbeth does murder sleep'" (2.2.39-40). Later on, at the banquet, Lady Macbeth comments on Macbeth's insomnia: "You lack the season of all natures, sleep" (3.4.142). So, in the mad scene in 5.1, Shakespeare has Lady Macbeth sleep, but not in a normal fashion. As the Doctor comments: "A great perturbation in nature, to receive at once the benefit of sleep and do the effects of watching." As the language here shows, Shakespeare emphasizes how unnatural and disturbing the actions of this husband and wife are, and because this tragedy is a psychological examination of guilt, we get insanity. Further, what is particularly striking about Lady Macbeth's guilt here is how cold and amoral she was at the beginning of the play. It is sadly appropriate that the woman who says "A little water clears us of this deed" (2.2.71) obsessively washes her hands before her death, probably by suicide.
Lady Macbeth speaks about the unwashable blood on her hands, the striking of the clock--suggesting that time is short for the reign of her husband as well as her own life--and her husband's reluctance to perform the very murders that she so regrets now.
The suggestion is that Lady Macbeth is too guilt-ridden to maintain silence, though when awake, she forces herself to do just that. Shakespeare well knew that conflicts have a way of working themselves out, or at least atempting to resolve themselves, when one is asleep. Her unconscious mind is extremely conflicted. It is also interesting to note that Shakespeare has Lady Macbeth speak in prose, which the critic AC Bradley noted is the way that Shakespeare often wrote for had characters in abnormal states of mind.
Freud said that there are no accidents; perhaps Lady Macbeth wanted to be caught. We never find out, however, She is dead soon after this scene.
One of the more fanous lines from Shakespeare occurs here: Out, out.... This is echoed by Macbeth later, and of course, used as the title of a Frost poem.
Lady Macbeth also refers to the murders of Banquo and the household of Macduff in her little rant.
"Look not so pale, my Lord. Banquo's buried. He can not come out of his grave."
"The Thane of Fife had a wife, where is she now? What? Will these hands never be clean?"
She also never leaves the candle, indicating that she is afraid of being in the dark--something that she relished on the night that she and her husband murdered Duncan.
It is clear with the dijointed and seemingly unrelated topics of her talking that she is "sorely charged" as the doctor puts it. Her guilt is overwhelming, and the fear she feels is even moreso.