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Since you were editing the specific users post, he have the right to approve your edit even though he doesn't have privileges to do so on other posts. This user doesn't have access to the Suggested Edit review queue https://sharepoint.stackexchange.com/review/suggested-edits/

It is a system generated flag. It is nothing that we moderators have control over :) Probably it runs in batches or as a scheduled tasks, and therefore the time before the flag appears varies (this is just a guess though)

One post can span all of the categories. This can be seen by a new user, providing a comment like "I'm having this problem too did you find a solution?" to an old post. This would result in it spanning all 3 categories. The queue in which you approve it will determine what point you get and the act of approving it from one queue clears it from the others.

I declined that flag (not the author), based on the fact that the answer was indeed answering the question. With out without the link / new update it is clearly intended to answer the question. Therefore the flag "not an answer" had no merit according to me. The "low quality" flag would have been a better choice, but if you ask me the answer was of a good ...

That answer was only reviewed by one person, not the author: https://sharepoint.stackexchange.com/review/low-quality-posts/66430 The review then ended early because the flag was declined. The flag was declined by a moderator though, not the author. The author of the post did edit, possibly in response to the review comment, but this wasn't done from review....