SO madness doesn't impart understanding... it's a result of understanding.
Sure, in a sense. But they're intertwined. You can't retain your sanity and understand, not as a human being in the Cthulhu Mythos. As you understand more, you slide into madness. You can't have the deep understanding without being "crazy".
But there are also hints of the opposite direction too - i.e. people who seem like they've always been mad, but who seem to understand the Mythos. Some shuffling tramp might never have been an Arkham professor or whatever, might always have been "off", but he recognises the signs of the impending apocalypse or the like. And frequently "primitive" or "feral" people, who have no training, no deep intellectual understanding of the universe, just some kind of implicit one, or instinctive one, and whose minds are already "mad" or "bestial" (and yeah there's a ton of racism in there, but let's skip lightly over that), also understand the Mythos.
In other words a lower san score doesn't allow for a better understanding it occurs due to exposure to the truths.
No. See my second paragraph (you edited this in after my first).
EDIT: And there's a point where you become a gibbering heap who can't comprehend anything and can't cast any spells. That's what more and more madness does to you.
Civilized men of the type that are the heroes of his stories become gibbering heaps, sure, yeah. Sometimes they literally become a non-human being of some kind. But we see characters who are not such men, who are crazed, but not totally ineffective (just usually totally devoted to an Old God or the like).