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.
Code:
## Various Multimedia Helper Apps Mplayer, Real, w32codecs, etc.. ##
deb http://debian-multimedia.org sid main
For tovid.
Code:
## 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