What's "less" in nevertheless and nonetheless?
Solution 1:
This may be simplistic, but surely nonetheless, nevertheless, notwithstanding (all adverbial conjunctions, I think) imply that the statement that is to follow (that which is about to be conjoined) is not any less true or of lesser value than the statement that precedes it (that which it is conjoined to by the conjunction). re Question #2, I don't think it's possible to break a word apart and track the etymology or function of that part in isolation. That leaves your Question 1, so far, unanswered.