What's the significance of suicide, talk of suicide, and self-harm in Macbeth?

The supposed suicide of Lady Macbeth in this play is not shown onstage; at the end of the play, in act 2, scene 8, Malcolm describes her as a "fiend" who "as 'tis thought, by self and violent hands / Took off her life." He does not know for sure that she has killed herself, but this is what is rumored. Earlier in the play, Lady Macbeth's doctor asserts that "more needs she the divine than the physician," suggesting that her mental illness is an affliction of the soul, rather than simply of the mind; accordingly, her "infected mind" seems to lead her to an unnatural death through which her soul cannot be purified. Given that Malcolm believes her to be a "fiend," it is fitting for him to assume she has killed herself; suicide was extremely taboo in Shakespeare's time, and it was believed that self-murder would keep the soul from God, as that of a "fiend" should be.
The vast majority of suicides in Shakespeare's plays are confined to foreign parts and Roman times, a means of avoiding the taboo. This suicide, committed on British soil, is significantly performed by the play's villainness, rather than by a heroine. There is no discussion of it beyond Malcolm's brief comment at the end of the play, but we can interpret from context that this would be seen as a fitting end. Lady Macbeth has been driven into madness through which she has enacted a divine punishment upon herself.
Lady Macbeth's doctor does not associate mental illness irrevocably with poverty of moral fiber—indeed, he says he has known sleepwalkers "who have died holily in their beds." However, Lady Macbeth seems "beyond [his] practise," and the juxtaposition of his comments suggests that she is far removed from those who "died holily." On the contrary, Lady Macbeth's guilt has become a physical stain to her: "will these hands ne'er be clean?" Her continual "accustomed action" of rubbing at her hands might be interpreted as a form of self-harm, an attempt to draw out, or eradicate, a stain on the conscience through physical abrasion of the skin.
The suicide in this play is only alluded to, rather than confronted directly as a theme. However, it is significant that it is enacted by a villainness described as an amoral "fiend" and that it is presented as the direct result of guilt created by her own actions, causing her mind eventually to collapse under the strain.