Don't know how much your school will appreciate you using your own
OS to boot into their computers. I guess this all depends on what exactly you want to do. But to maybe answer your questions:
1. Yes, if you can set the BIOS to boot from an eSATA.
2. If your home machine has Vista on it, use the XP. I don't think you can use two instances of the same copy of windows simultaneously.
My suggestion would be either 1) Visit
PortableApps and try to find the programs you're wanting to use and install them on your external drive or, 2) get a Linux Distro and install that onto your external. You can pick up distros of Linux that are already tuned for media and such... but I can't think of any off the top of my head.