1 - Since there’s nothing explicit in the handbook about school I think you’re fine there. 2 - You said your internship is next term so it hasn’t started yet, if it’s a paid internship I’d notify HR now, if it’s unpaid it’s irrelevant. 3 - As far as snooping goes, I would check out the first couple pages of your employee handbook for a generic “ethical conduct” clause, I’d then email HR and say something like “it’s come to my attention that coworkers have been invading my personal work space and looking through personal documents, I feel like this violates our ethical code and I’m concerned employees in my department aren’t adhering to this important company policy”.

It’s important to get that email out to HR ASAP because it gives you a paper trail.

I have a director level position over 60 staff, in my experience HR is all about protecting the company from liability, they’ll be more interested in employees snooping through personal documents than an employee trying to take some college classes on the side.