Moderators have no way to access any regular conversations they aren't a part of.
(Content moderation conversations created by the moderation panel can be viewed.)
Well, basically anything that violates the CoC. (That includes rightout illegal actions.)
E.g. if someone starts a conversation "Do you like cute cat images. See this one," and when you click on the link, you're facing a dick pic.
If content is reported, the chapter, comment, or profile (including the most recent comments) is captured.