MP4 is video. I first saw the format on iPod/iPhone video, but it's in wide use now and not just with Apple.

There should be software that can transcode AVI into MOV or something else. As I said, AVI is just the container format, and it is a "venerable" old format - you can translate that into "old and crusty" - it doesn't have nearly the features that newer formats have. That said, MPG is even worse. Proper modern formats like MKV and the like have much better support for modern features.

Apple tends to get really uppity about using formats that they don't like - they get into their "well, you should be using non crappy equipment then" mode when you complain, rather than making their stuff play well with others.