I suppose, but I don't make much money from my site and cheap hosting doesn't really cut it. If I wanted to do everything that I want to do I'd probably have to go for a cheap VPS service and that's not exactly "cheap" in terms of web hosting.
http://www.lowendbox.com/If you look around, you can get a vps for as little as 2.50 a month. I just got a vps last month for 7 bucks a month that has 750gb bandwidth, 20gb storage, and 384mb ram.
As for your first question, I would say it depends on the university. At my uni each student registers their computer on the network and is assigned an ip address visible to the outside world. We also can register a hostname along with it, which is just a subdomain within the school's .edu domain. Because no ports are blocked, we are free to host whatever services we want. The biggest limitation, though, is the upstream cap of about 120kbs.