3 phase AC motor 220V powered from 12V battery
To actually answer the questions:

1) The efficiency is most certainly changed when you use a capacitor so generate a phase shift.  The winding's magnetic field is going to be reduced.  It will get it turning in the right direction, but not efficiently.

2) Yes, you can (and do) regulate a three phase induction motor's speed by controlling its frequency.  They can run (with simple Volts/Hz control) down to nearly zero speed while maintaining decent torque, and up to beyond base speed as well.  But, your capacitor phase shift isn't going to like variable speeds unless you use an absolutely huge value capacitor, which is going to be difficult to find since it has to be non-polar.

3) The most common early AC Variable Frequency Drives (VFD) used a totem pole of SCR's to generate a six-step waveform that went to the motor.  These had little impact on the actual driven motors windings.  The newer drives do need motors with a better rated insulation system since newer drives use a high frequency PWM waveform to generate the low frequency output to the motor.  Older insulation systems don't like modern high frequency waveforms.



All that being said, you would be better off with a simple 12V DC motor.  If you MUST go AC, and need variable speed, build at least a full three phase inverter, even if only using 6-step technology.