Those ports are probably blocked because the school doesn't want what uses the ports using their network. Several schools have gotten letters from RIAA themselves, so they're cracking down on sharers. There's also the issue of bandwidth usage; an innocent little "I'll let you and your friends download the songs on my computer" can quickly spiral into the whole world hitting your computer, with a huge drain on bandwidth for the whole school. I know one university computer security manager who's fighting with a user in one department that's mirroring the newly released Red Hat 9.0 distribution-talk about bandwidth hogging!
I'm not saying that you shouldn't expand your knowledge or anything like that, but be prepared for any consequences violating the school's network use policy may result in.
As for how a proxy works, you direct all requests to the proxy, which translates/filters the requests and manages replies so they go to the right computer. I don't know of any Mac proxy packages off hand, but there are bound to be some.
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