Arduino board to control microwave oven?
It's pretty much all proprietary. It can be done, but you'd have to replace all the circuitry with the Arduino, interfacing with the existing magnetic and mechanical devices and doing everything in your own code.

Power level is controlled by PWM, but it's extremely low frequency PWM, on the order of 0.05Hz (20s period). That's why there are two different sounds that come from the microwave when it's not at full power; one when the magnetron is active, and one when it is off.