mp4 files are typically used for videos - so are you really asking whether the Photo Album could be used for videos (not just in mp4 format)?
Currently the Photo Album doesn't support videos. I guess it could make sense to add this, as videos are increasingly popular! I'll add it to the suggestions list. If other people would like this too then adding your support here is likely to accelerate its development!
On the second question - no I'm afraid it isn't possible to copy/move files between applications, or between the Assets Library and applications.
Just piping up to say that being able to add videos and photos in the same gallery would have been really useful today. We're running a creative competion and there has been a video included. It would've been lovely to have been able to add it in the same way as the pictures and showing in the related images gallery.
Having said that, it's not something we do often!