Is it possible to have an AC motor with only a partial stator, one that does not fully encompass the rotor? Refer to the picture to understand what I mean. This would be needed to drive a spherical tire of a car.
It's certainly possible - I built one many years ago to allow a cutaway model of a power tool to run. Bear in mind that a C shaped stator would produce significant radial forces on the rotor shaft if you're trying to produce a lot of power with it, and having two opposing sections of stator, i.e. with a symmetrical gap on opposite sides would balance out the radial forces - but reduce the amount of power you could produce for a given motor size.
Yes, although getting efficiency out of it may be quite difficult. Conceptually, you may want to start with linear motors, and go from there.