Thanks Toritoribe.
1. Yeah, I meant 辞める. So, the action he wants to be allowed to perform is クィヂッチ・チームを辞める, right?
2. Yes, it should be 控えた. That makes more sense to me with ある日, but I still don't understand 一週間後. As far as I can gather this part is supposed to mean "(one day) about a week before the exams were due to start". I can't figure out how 後 fits into that meaning.
4b. Does the "also/too" aspect of the meaning refer to the fact that other things are also written in the books?