1. - "DVD component input" is more of a marketing lingo that most TV manufacturers use these days, they're just known as component video input.
- Component video uses
3 cables for transmitting video data vs just
1 cable as in Composite video and thats a primary advantage for Component video to show significantly better video quality. Even S-Video is a variation of component video (it has separate wires for luminance and chroma like Component video), but has only 1 cable and hence is not able to match up to Component video again.
- The 3 cables carry data in different "Color Space" formats : either in the RGB format (Red, Green, Blue) or YCbCr (Y=Luma component, CbCr = Chroma component) or YPbPr (similar to YCbCr).
- The advantage that Component video has, comes into play mostly in HD (High Definition) media such as DVDs, HDTV broadcasts, etc. Component video is able to support high resolution formats such as 480p, 720p, all the way up to 1080p. S-video generally can manage only resolutions upto 480p , composite video can barely handle even basic HD media.
2. Not necessarily, as I mentioned earlier its just marketing lingo used by TV manufacturers to get people to think only a certain class of TVs can play DVD's. Most DVD players will have Composite video output, S-video output in addition to Component video output. So you can use the output that your TV can support. Generally Component Video > S-Video > Composite Video.
3. Havent tried, so cant comment. You could check this thread for results :
http://www.techenclave.com/forums/7800gt-with-hdtv-too-crazy-63831.html