1. No. Not enough power.
2. I don't know. How many watts does the G4 tower require. Consider an inverter.
3. Yes. The G4 will have the same shortcomings as the Mini. Your just exchanging one set of hardware for another. The underlying operating system and applications are the same.
4. Considering that you thought the Mini was hacking in on your free time, this one ought to be a real sinkhole.
You don't really state why you didn't like the Mini install, other than to say that the AVIC seems to have fit the bill. I'd say that it gives you good quality sound, GPS, video, and whatever else the AVIC does. How does adding a G4 tower to your car add any features that the Mini didn't?
It sounds to me like you're covered. Leave the tower alone.