Yes, given the right circumstance, I think a quote could stand alone as a good answer (provided it actually answers the question).
But for me personally, I always like to add some kind of extra explanation or context. I recall one question that simply asked something like "Is C♭ to A♯ a doubly augmented sixth?" The answer was just "yes," but it seemed more proper to show them the logic of it: here's a major sixth, then an augmented, and so here is why it's a doubly augmented sixth. One thing I often ask myself when I'm writing an answer is: "If this answer is still confusing to a reader, what else can I add to try and walk them through the process?" It doesn't work for every answer, but it's served me well in the past.
And no, I don't think the source of the quote matters, although I think we should always strive for the most reputable sources; all things being equal, a quote from a textbook will be better than a quote from Quora. To me, the democratic aspect of Stack Exchange will save the day. If the information is bad, the community will (hopefully) downvote it and upvote a more proper answer.
And proper citation is actually discussed in the help center; the Referencing page explicitly states that plagiarism "is frowned on by our community, and may result in your answer being down-voted or deleted."