Well, I went to a huge university, and I have to agree with disney20038 in that it really did feel like it's own little world. Classes were spread out among a number of buildings, and actually, there were sections in a way (the arts buildings - including art, music, theatre, languages, social sciences, history, etc - were at one end of campus, the sciences - including physics, chemistry, biology, computer science, maths, etc - were in the middle, and engineering along with some other minor faculties were at the other end... I don't remember where human kinetics ended up, but they were probably in the middle section) (oh yeah, and business was kind of in the middle too). The arts buildings were the oldest/least updated, while some sciences buildings, the business building, etc, were recently updated/brand new (as you can imagine, alumni graduating from certain fields donate more money than those graduating from other fields!).
There are a number of libraries (usually specializing in a field of study within that field's building). There are many places to get food from. And coffee. There's a student building where clubs have their offices and includes a student-run movie theatre that shows older movies a few nights a week. And a building that's the go-to for financial aid. There are a number of buildings for sports (basketball courts, ice rink, pool, weight rooms, etc), and also fields for sports too (football, soccer, track, etc).
As for rooming on campus, there are different residences (mostly on the outskirts, but one in the middle), consisting of a group of buildings together. Two of them (of those groups of buildings) are geared more towards the newer students (1st and 2nd years), and are dormitory style (some shared rooms, some single rooms) (those have a common building in the center where there's a cafeteria... they can't cook food in their rooms). There are three or four that are geared towards older students (at least 2nd year and beyond), and those are more apartment style (where you live with other people in a unit, but you each have your own lockable room and shared kitchen, bathroom, and common space). I think one is specific to grad students. And there are a couple of residences that are for families and/or staff (like professors, other people who work on campus, etc).
In the university I went to, the highest position was called "chancellor", but I don't know if that's what they're called everywhere. And I only met the person very, very briefly when I walked across the stage to receive my degree. You're more likely to interact with your department/faculty head than the head of the university (especially since they're the ones you need to go to when wanting advice on courses to take or help planning your degree/academic career). And disney20038 mentioned teachers are "professors" -- that was most definitely the same in my experience. I addressed my teachers either as "Professor So-and-So" or "Dr. So-and-So".
I can't think of any fanfics set in university to recommend.
If you're looking for further information, my suggestion would be to take a look at some university websites. Look in the "students" section. There should be a list of courses somewhere, if you're interested in seeing what's available. And a calendar that shows the start dates, the last dates to withdraw from courses without paying for them, the exam period dates, and breaks (like winter break, reading/spring break, etc). They might even have info on housing if you're interested in looking into that at all. Well, I hope this helps! Good luck with your story!