The easiest way to do this would be to precompose your footage, then animate it inside your precomposition, and finally add your mask on the precomposition.
If you're not familiar with nesting & precomposing, I recommand you to read the dedicated help section
Hope that helps
You can use the pan behind tool (explained in the help section) or any shape layer or masked layer as a track matte. As was stated before, the track matte is probably the easiest solution.
Tracking a logo to a moving belt involves tracking and corner pin. If you can't track the belt, then you'll have to set corner pin keyframes by hand. Corner pin is also covered in the help files and if you Google AE Corner Pin Tutorial you'll come up with a bunch.
Making it repeat is as simple as duplicating the first corner pin layer then moving it down in the time line.