It will be absolutely fine to play an xbox on your plasma. Just avoid leaving your xbox on for several hours with the same picture on the screen (like pausing a game and leaving for 2 hours), there is a small possibility that the image will be burned onto the screen.
Chat with our AI personalities
Not as good as you would have with an HD TV, but graphics will be slightly improved from the original XBOX. In my opinion.
An xbox, A game, and a controller... ---EDIT--- and a tv, and all the xbox cables
No
you must have a HDMI cord hooked up to your TV to play splitscreen.
You need a HD "High Definition" TV.