That is probably the coolest idea I've heard in a while! If it doesn't show already, 'droid fan here lol
As far as the power source is concerned, you could mount a switch outside of the mounting area so to toggle on/off the power-line to the tablet before/after the engine is running. You could hide it anywhere, but I'd keep it close to the unit to avoid any (even minimal) power leaks/drops. Unfortunately, I don't think you would be able to use the steering wheel controls on the tablet directly. The only way I can see those working is if you keep the stereo in place, and you only use the tablet as either external storage (if you can use a USB connection on the existing stereo - which I doubt) or via the 3.5mm stereo output on the tablet, connected to the AUX of your stereo. If anyone knows of a way to do otherwise, please say so: I'd use external audio controls on a 'droid tablet in a heartbeat!!!!! As far as I know, this would depend A LOT on Android drivers to work...almost all newer android smartphones have the wired headsets with mic/buttons combo: maybe something like that would better suffice your situation? Look into the Dell Streak 7. I know it's not the bast tablet, but just as an idea....
Hope I didn't lose anyone in my rambling, and please please please don't destroy me if part/all I mentioned above is wrong! To my knowledge, it is not
Hope this helps!