When I survey a DVD (not HD) on my computer, at what resolution does it play? The resolution of my monitor?

Answer:

DVD's are encoded at 720x480 (NTSC) or 720x576 (PAL). If you play within full screen, the computer is upconverting the signal to game your monitor (with either the distance from the ground or width as the max).
I depends on the setting of the video player, but the maximum resolution that it can play at would be that of your monitor.