Flagging a post as spam/offensive makes the Community user downvote that post.
Does the same thing happen with the "very low quality" flag?
The Community user downvotes a post with no upvotes if a moderator marks a VLQ flag helpful (example, requires 10k on Workplace). (I was puzzled the first time I saw this happen.) Community does not vote just because a flag is raised, unlike with spam. It appears that the automatic downvote doesn't happen if a VLQ flag is validated through the review queue (example).
It's rare for a helpful VLQ flag to not end in deletion (at which point the vote doesn't really matter any more), but it happens.
Nope. Try for yourself; it shouldn't be hard (on Stack Overflow) to find a post which warrants a Low Quality flag. Flagging won't change the post score.