Yes the 12v coming into the shield will power the Due. It will only be powered when the ACC line has power, otherwise the shield will be in standby mode, and the Due will be off.
If your tablet can get enough power without the Y adapter don’t use it. The Due will provide power to the Android. But with your stereo unit, it get’s it’s own power from the car correct? The USB is really just data in your case.
Once I get the input and outputs all finished (SOOO much code :S) I’d suggest you hook the stereo line up to one of the shields outputs. Then you’ll be able to configure the stereo to stay on even when the accessory line is turned off. The timeout is configurable within AutoSense. You could also configure things so when the door opens the stereo and Due all turn off.