If a user submits a suggested edit, for example from the First Posts or Late Answers, and their edit is not accepted, does that affect their reputation? In what way?
The system does not distinguish suggested edits* made on the Q&A pages from those made within the First Posts / Late Answers review queues. In both cases, an approved edit gives you +2 reputation and a rejected edit doesn't influence your reputation.
*: I assume that is what you meant, since other review actions can't really be rejected and in any case don't influence your reputation (apart from downvoting answers).