I'm going to a friend's house for a couple of days, and I've got a big file downloading in BitTorrent. I was wondering if I shut off my computer will it resume my download next time I turn it on or will it cancel it?
Yes it will resume next time you start up bittorrnet. The way this works that the next time you open bittorrent from your friends house is that bittorrent will recheck the file to see what pieces it has and what pieces it still needs. (so if the file like 8gb or 12gb it may take a will to recheck it)
Use another BT client, uTorrent comes to mind. It can keep track of all your torrents, allow you to control how much bandwidth you provide globally/to each torrent, as well as pause/start/stop.