it doesn't have to have GPS or be connected to anything to work.
i mean, thats not how they work now. its a feature some cars use, but like, the battery and computer (and sometimes gas) make it go. its still a car.

and for 2
thats not how GPS works

and for 3
fixing the car will be the responsibility of whoever makes them. (if you wanna keep the phone analogy going) Ideally you wouldn't own a car. its just a robot uber. In a perfect world, we'd all just have better public transportation and just use autonomous cars to replace delivery drivers.