I'm not a pro but I'll tell you what I know. My computer is setup exaclty how yours is. I use a 19" monitor for computer stuff, the TV is right next to my computer and s-video is always hooked up. I have 2 sound devices (integrated crap and Sound Blaster 5.1). The integrated crap is hooked up to the TV speakers and the Sound Blaster is hooked up to headphones.
Video out on the video card does not send sound signals.
Yes composite are those RCA ones.
No normal video card has a cable TV connection. I think ATI All In Wonder cards have those but those cards are just insanely expensive.
Now about the sound thing. I know you can switch between the different sound cards but I don't think you can use both at the same time.
Switching between sound cards is easy, just go to control panel then sound.