Using bittorrent technology is legal;
what you download via that technology may not be.
Your IP address isn't necessarily unique, and ISPs randomly assign IP addresses or else they'd run out of them - but they have heavy logging and databasing to know which IP is assigned to which subscriber at what time, and that can be easily cross-referenced with the webpages requested. Sysadmins can see live traffic and also scan back through the logs, and they give this information over to law enforcement whenever it's requested.
Furthermore, using Tor may hypothetically get around that - but don't count your chickens: Your ISP knows when you use a Tor client and this often can put some type of flag on your account. Plus, unless you use Tor on a computer you've never used for anything other than Tor and you've only used it at a public access point it can be tracked; Tor traffic is anonymous when it's being transferred, but the endpoints can be recorded and that's how Tor users can be found out.
Even then, gardon-variety websites can track tons and tons of stuff that makes you unique -
https://panopticlick.eff.org is a cool way to see just how unique and trackable your system is - even down to how many and what fonts you have installed all contribute to making your footprint unique - and if your computer footprint is unique, then it is trackable. In fact, the unique factor could simply be low
enough (e.g. less than 100% unique) and they'd have a pretty good idea it was you based on browsing behavior patterns.
But that's all academic because your Alma Mater may just restrict access to certain thing, or even block sites by keywords, and they're within their right to do it.
Just because it's the US government or Google invading your privacy doesn't mean it's not 1984 all over again in 2015. In fact Google probably knows more about you than your mother does. Or the NSA.
It's the seeding that is the problem I would think. Legal or not, you shouldn't be distributing content to hundreds to thousands of people. It's a waste of their resources, especially if everyone is doing it.
I seed a little bit. If I'm paying for my internet, I expect to be able to use it - for uploading, downloading, sideloading, backloading, whatevers. I'll stop the seed once the download is done though, and if I like the music I torrent I'll go buy it. There's no way I'm paying the price-gouging executives when I haven't heard the song all the way through... they pay pennies on the dollar to the artists anyway - and then whine about how they're being victimized. Yeah, right.