1. Can also be called a Media Center PC, if you like. Main purpose is to connect it to your living room TV and stream media to your TV.
2. Nothing different, but something more than a normal PC. Depends on how you build it. Most desired ones have wireless keyboard / mouse.
3. It can have HDMI. Yet another desired feature to have Full HD capability. But you can also do away with Component or DIV.
4. PC and depending on your location, a TV Tuner card.
5. Build it, preferably. There are ones available (Eee box, I think). Something similar to HTPCs are MVix, TVICO, etc. But to have a true HTPC, your only option is to build it as the manufactured ones might not have TV Tuners specific to your country.
6. Depends on what components go into it, but definitely less than any Gaming PC. An AMD and 780g based graphics solution is ideal.
7. Should be low power. Fanless, if possible. Silent.
8. Haven't worked with Linux or other distros, but Windows Vista Home Premium is my choice.
9. Dunno. Don't get Digit here

Maybe someone from India can answer this.
I don't find the thread anymore, but look for choto cheeta has a good article here:
http://www.chotocheeta.com/2008/07/2...dia-center-pc/