1. PWM Time-base is the clock source around which all other PWM timings are based. Its the clock that clocks all PWM operations.
2. PWM resolution is how accurately you can set the PWM duty cycle. It determines the "minimum increment" of on/off time for the PWM duty cycle. The more bits you have, the more accurately you can set the duty cycle. For a given IC, this available PWM resolution changes with PWM frequency and other factors.
3. You want the PWM pulse to be as fast as possible so that the motor won't pulse and waste lots of energy, but you want it as slow as possible so that the power MOSFETs don't switch back and forth too often or too fast because it takes time for the MOSFET to switch on/off and every time it does, it must pass through an lossy intermediary state between no conduction and efficient conduction. So the more you switch, the more time is spent in this intermediate on/off state and the more power is lost. If you switch at an insanley fast rate, the MOSFET might not be able to react fast enough to change states and may remain locked in an on/off intermediary state. 20kHz is a good number to go by for most things.
4. I think complimentary PWM is when you use two pins and one line pulls low and the other pulls high alternately...or something like that. I am not entirely sure myself.