Last I checked the short answer is no. There's very little control over video playback, it's definitely one of the more disappointing limitations in the SDK.
Okay, so it isn't possible to loop it without a slowfade out at the end, but I did figure out that it IS possible to loop it with a fadeout simply by calling play again once the video is finished...
Don't know but I have seen this problem in both the example app provided by app AND in my own program. I am also looking to loop video and MUST be able to do it for my app to make sense. You can somewhat hack the movie player to do things like play video non fullscreen etc, but I believe these are so called "Private APIs". A class deconstruction is here:
Lets solve this issue, to be honest I am very disappointed in the, well relatively pathetic video APIs that are publicly exposed. The reason Apple insists that everyone play movies their way, in a fullscreen landscape view... I mean why??? Its pretty ridiculous.