They make small, light, powerful motors for model planes; it should be doable, and the weight would not be prohibitive (an extra 4-500 gr perhaps).

They would be situated under the bridge, inside the body, and that is where the tuning would be done, like in some electric guitars without a headstock. Easy. Though there may have to be some sort of construction to minimise the dampening effect that the motors would have on the sound, being attached to the body.

Small keyboard on the top side, where the pre-amps usually are.

All that is easy. The killer is the power. These motors would consume power like nobody's business. Tw AAs or even a 9V battery wouldn't cut it; and that is where the weight might come into play. Unless...

...you could run the motors off Phantom power (and you plug the guitar into the amp with an XLR) - but that means the system would only work plugged in, which is only half the job done. Anyway, I think Phantom power would be insufficient in all likelihood, so back to the batteries. Unless...

...you plug it into the mains power. But the safety issues then take over, with 6 wires ready to fry you should something go wrong with the insulation.

You could of course install a tiny wind generator in front of your mouth to power it as you sing...

I'll get me coat.