Not all mp4/mov files are the same. There are numerous audio and video codecs that can be used to create either and they are not all playable on a stock Android system. Sometimes you can find an alternate player or codec that will allow you to watch them. Sometime a format conversion is necessary.
My guess is, anything you purchased from iTunes will have DRM. Just one more way in which Apple chews it. Tampering with DRM on any file is illegal.