Learn English – Use of prefixes mis- and mal-

I don't think that it's the same prefix as much as it is the remnant of a number of different grammaticalised pre-fixings. Most of them seem to have happened during the period when then curious admixture of French, Viking Danish, Anglo-Saxon and a sprinkling of Gaelic were distilling themselves down into the various dialects of Middle English. The spelling's kind of arbitrary, but a is the letter we tend to use when a word starts with a schwa that's flatter than we'd represent with a short e.

English was essentially an unwritten language during that period (and the population essentially illiterate), so it could be a time of great flux. A lot of words were repartitioned. All one became alone, the n sound migrated from the ends of words like mine and thine to become the initial (and previously non-existent) consonant of words (especially eke names -- thine eke name also became thy nickname) and so on.

As with a lot of what happened during this period, what we have now in the language is mostly what was present in and around London when the orthography was fixed by printing. Many of the a- words that one recognises as quaint regionalisms today (like a-hunting) were standard in dialects that did not, themselves, have the good fortune to become the standard themselves.

As for new words, well, printing (and general literacy) sort of put a stop to arbitrary movement of word boundaries. A question was posted here earlier asking about the meaning of "grab a hold", and it didn't take long for somebody to reply that the phrase was actually "grab ahold" (something my spell checker has decided is a problem). I would bet that "grab a hold" or "take a hold" (hold being synonymous with handle, as preserved in hand-hold) was the original phrase. They sound the same, and if you hear a hold often enough without seeing it written down, there's no real reason why you might not think of them as a single word.

Prefixes are morphemes that are attached to root terms to create a new or more complex concept. However, the root term can have many variations, and a given word that contains a prefix may not make sense if the prefix is removed.

Your example of promote is one of these. The following is the explanation of the etymology of promote from the Compact OED

late Middle English: from Latin promot- 'moved forward', from the verb promovere, from pro- 'forward, onward' + movere 'to move'

Many prefixes were already attached in the language from which the word derived. This is an example. Movere (to move) is the root and pro- (forward) is the prefix. Promovere was an acceptable term in Latin before it migrated to Middle English and modern English.

Some of the derivative words in English can stand alone when the prefix is removed, such as promotion (pro + motion = forward + movement).

Even if the word was created in modern English by adding a prefix to a root, the variations on the word may not allow the root part to stand alone when the prefix is removed. For example, telephony is a term that was created in modern English. If the tele (distance) prefix is removed, the root part phony cannot stand alone. However in telephonic, when you remove the prefix, phonic can stand alone.