No but you can't get audio though DVI. And there may be an issue with some protected play-back. If your video card has HDMI output, I'd get an HDMI monitor to cover all bases.
Will not be any difference. Most response times like contract ratio, are not very true ratings, manufacturers tend to measure different things. Anything around 10ms is pretty much undetectable.
For games, the lower the response times the better, generally speaking. There is no real difference between 2ms and 5ms. Some people can tell the difference while others can't. In a nutshell, the lower the response time, the less likely you will see ghosting issues.