to me, you are a kid. It is not a condescending term, a disparaging term, or a derogatory term. You need to settle down so you are not expelled from school because it sounds like you really need to continue your education so you can figure out your ass from a hole in the ground. (and yes, that was a condescending statement)
your question about what is legal or illegal. I said exactly the opposite of what you just asked.: a young person; especially:child —often used as a generalized reference to one especially younger or less experienced <the kid on the pro golf tour><poor kid>
only if the rules of the school say you do1. Do I have a legal right to an appeal and hearing as I would if I was handed a city citation?
private property. A State school is one subsidized by the state and often governed by state administrators. It is not owned by the state. Just a continuation; even when dealing with actual public property, you still must comply with any rules or laws put in place by the governing entity. Public property doesn't mean it is "your" and you get to do anything you want to do.2. Because it's a public university is it public property, private property, or some weird gray area?
yes, they would. Could they enforce it? Likely not unless there was actually some notice of he rule given but along with that, they can demand you never set foot on their property again or face trespassing charges if you do.3. If I wasn't a student would the university still have the authority to issue me a ticket, claiming that I should have read the student handbook before biking through a public university?

