OK, First let me say, I don't have HD anything
I just know a little bit about it.
Yes, most, maybe even all of the HDTV tuner cards support standard cable TV also.
If you are recording a TV channel, a single tuner card, can only watch what you are recording, If you want to watch a different channel than you are recording or record 2 channels at the same time, You will need 2 TV tuner cards or 1 dual tuner TV card.
The TV cards only have the channels a TV would have, So if you want to watch channel 500 you need to set your cable box to channel 500 and your TV card to channel 3. If you buy this Vista HDTV tuner card with cablecard, you don't need a cable box, It's like a cable box for your pc, Obviosly your cable company needs to suport cablecard for you to use it.
Whatever graphics card you buy, Make sure it has HDCP support. Your monitor will need to support HDCP also (post 2 has the info)
From what I have read, DVI to HMDI will be the same quality as HMDI to HMDI.
The HDMI video cards are all DirectX 9 right now and only a few support HDCP But, most of the HDMI video cards have a SPDIF(digital) audio Input, This makes it possible to run the audio from the sound card into the video card and pass it though the HDMI cable to your TV. This is nice because you will only need 1 cable running from your PC to your TV. So if you get one, Make sure your sound card has a SPDIF output.
HDTV also has digital sound, 5.1 surround sound or something like that
The 8800GTS is overkill unless you will be gaming on you HTPC. Idealy the best video card for a HDTV HTPC would be a DX10 HDMI HDCP video card, But they don't exist yet.