Well, how many teachers are really going to question students wanting to hang out in the library? My teachers would have been completely down for it. As for Faith being there, and renting a motel, I always thought she was a little older, 16 or 17, in the third season, so it wouldn't be that questionable to rent a motel room. For all the managers knew, she was emancipated from her parents. Also, she could easily pass for 18-20, so it's not like they felt an obligation to call child services. And, most teachers wouldn't realize she WASN'T a student. Sunnydale High is a big school, comparatively. You don't necessarily know all the students.
The Watchers Council probably pulled strings for Wesley.