Well the only thing that I have every been able to get to capture a good video signal to .avi is Xdtv but I can never get it to have sound but apparently that is limited to the card you are using from what I have read so you may be lucky and have a card that will do it. For conversion to dvd I have had really good experiences with tovid a rather simple to use set of scripts/gui front end. Never actually seeded a bittorrent but almost any client is able to do seeding I use ktorrent for my downloads but have used rtorrent from the command line in the past it works well. For the xdtv you can get it with this for Debian.
## Various Multimedia Helper Apps Mplayer, Real, w32codecs, etc.. ##
deb http://debian-multimedia.org sid main
## Tovid linked from http://tovid.wikia.com/wiki/Installing_tovid
deb http://packages.kirya.net/debian/ unstable main contrib non-free
deb-src http://packages.kirya.net/debian/ unstable main contrib non-free