I'm sure it varies by department/university, but the police at my not-very-big urban university had it's own force comprised of sworn county police officers. That empowered them to give speeding tickets on the public streets through campus, and they were able to have very good response times to campus emergencies. I never had negative contact with them, but that's anecdotal.

The medical campus had emergency buttons on blue poles, and if you pressed one, you'd get like 4 or 5 emergency responses. Campus police, city police, and 2 or 3 of the hospitals had security or police on site.

I wish. Most of this force is criminal justice students, with a few GAs, and a few professional supervisors.

I have heard they have a pretty good collaboration with local municipal police, so anything happening on the campus could be passed off to them if jurisdiction issues arise.

It depends on whether or not the campus police can arrest and carry firearms. If not, then yes, its usually unarmed students and employees.