There's a cost to supporting IE6, and a cost to not supporting it. Depending on what you're doing, it might make much better sense to do something like:
Not really. You obviously need to take care of the height too and it must depend on video dimensions. Other players out there are designed for fixed widths.
Sure, but taking care of other parts of the player needs to be taken care of. Not that it's hard but it's surely not a feature of video players out there.
Love it, certainly going to use it when I need a video player. It even has full screen!
Edit: Even better, it's responsive to browser width changes!