Torrent downloading is not safer; that was what I was doing when I got the notice from Comcast. However, torrents can be found all over the internet, rather than on just the Gnutella network.

More info here: Beginners Guide to using torrents.

Port forwarding is described in the above guide. It will speed up downloading, but it is not required.
Some movie torrents arrive as a number of .rar files. For those, just right-click on the first .rar in the list and extract the file. Within a few seconds all of the files will reassemble themselves into one or two .avi files.
Most torrent programs include a search feature. You can also search for torrents via your browser, (Google, etc.), and there are a few sites that will search multiple torrent sites for the files you seek. (For files you find via your browser, after you click "download this torrent", click "Open" - not "save", and then you will see the file appear in your downloads window).