What is the origin of 没 as an alternative to 不?
This is a knottier question than it first appears. The answer is hard to summarise, but it seems to be related to the special status of 有 and 無 from the beginning of Chinese.

In the Old Chinese of the oracle bones, there seems to be fairly neat system of four. 不, 弗, 毋, 勿, where each of these is a combination of p-type vs m-type, reflecting non-modal (uncontrollable) vs modal (controllable / volitional) respectively; and vowel-final vs *ɯd final, which reflects stative/eventive/passive vs not. There was also 非 as a straightforward merger of a p-type with the verb 惟／唯／維.

Discussions of oracle bone Chinese often keep 亡 and 無 to one side, as they are verbs with negative polarity, and they replace 有 in negative sentences, rather than negating it. [Look in the 詩經: 亡 and 無 rarely paired with 有, and the two times 無 is with 有, it has a "futurity" about it, similar to modern Mandarin 不要 or 不會] We thus see that even from the time of Old Chinese, 有 was already a bit "special", different from other verbs. Compare Tibetan མེད med, the negative form (and not particle / prefix) of ཡོད yod, to be / exist (used in the construction for have).

According to Chappell &amp; Peyraube (2016), 沒 was used before the Yuan, and only appeared with 沒有 from the Yuan onwards (specifically by 1350). It had been "semantically extended" from its root meaning of "sink" via "disappear", replacing 無 and then "extending to an aspectual negator or a marker expressing a perfective negation".

We see that in southern varieties of Chinese, negative equivalents of 有 (rather than negative adverbs) still exist: e.g. Min 無 (Southern Min POJ: bô, Fuzhounese BUC: mò̤); Cantonese 冇 mou5 (with a different tone to the now literary 無 mou4), Northern Wu 嘸沒 (Shanghainese hhmm meq). Interestingly, Xiang varieties generally use 冒得 instead of a cognate of 無 on its own for the negative of 有: an example of suppletion; 無 is still used as a perfective with verbs though. 

So there is just something about 有 and 無 that became amplified with its use in the "perfective" through Middle Chinese.