The Process starts as soon as the ECU get power, if u leave the key in ON position without cranking & rotate the Engine via hand it will try to synchronize but again it will reset the position status bcz cranking speed is too low for synchronization & there is no consistency in rotation.
In case if the Engine is Off nothing wil happen, as there is no power to sensors + ECU.
Yup it synchronize itself every time when u crank the Engine. there is no ignition & no fuel injection for atleast one complete crank shaft rotation (360 or some times 720 degrees) ECU only concentrates on synchronization process. as u know accurate Engine position playz a vital role.
Yup it forget about the Engine position once u turn off the Engine, it stores the Position track in a volatile variable, only it remembers LTFT & some error codes.
Yes it wastes initial 1 or 2 crank rotations
Lets assume Engine is cranking @ 300RPM, (Frequency = 5Hz, to complete one crankshaft revolution it requires 200ms)
During Cranking most of the ECU performs Batch or simultaneous Fuel Injection triggering & extended Ignition Pulse (High @ extreme advanced position & then goes to low @ extreme retard position). Once the RPM crosses the threshold of 400RPM everything becomes normal,
Fuel Injection: Sequential firing
Ignition: Constant pulse of 2/3ms