Are you asking if the car should continue to play from the point where you shut off the car?
It does that for me when I interrupt a song from the USB stick. Not sure if that's the same for on-board HDD stored music. As far as I can recall, it did the same for music CDs (only played like one or two CDs in the car a LONG time ago... I do know that the car also remembers to continue from the last point played on all the DVDs (changer and single drive).
As to storing movies on the on-board HDD, I don't think that's possible (also because BMW would get into legal issues about copyright protection, etc). Besides if I remember correctly, there is only 12GB of free space on the HDD for you to use. If you are lucky, you might be able to store like 3 movies on there ...
I do know for a fact that you can't play any kind of video files via the USB either
At least it wasn't possible when I tried that about a year ago and I don't think they have or ever will change that (although I hope that one day this will be a possibility...)