If a user writes a post that gets marked as "spam" or "rude or abusive", he/she loses 100 reputation. Does this also happen when the user suggests an edit that gets rejected as "spam or vandalism"?
No, this doesn't happen. I'm sure somebody would have noticed and/or complained about it on Meta, and it's not listed in any of the questions here, including the FAQ.
It would take only 2 users (or even 1 in case of the author reviewing the edit) to impose this penalty on the user who suggested the edit, that seems too prone for mistakes (or maybe even targeting a specific user).
Largely speaking, all of the rejection reasons have the same effect. The exception is that suggested edits rejected as spam aren't visible for anonymous users.