In a sensorless system, the controller measures induced voltage on the non-driven phase of the motor to determine where in the commutation cycle it is. For startup, where the speed is zero and therefore no induced voltage is present, a special startup mode is needed. There are several different techniques for starting up reliably. The simplest method is to just commutate blindly at low speed for a while and see if any voltage appears. This technique will result in limited startup torque, and may even cause the motor to turn backwards a few degrees just as it starts.
Very similar, but they don't use a sine shaped drive. At partial power, the current is modulated, but the frequency and duty cycle remains constant through the whole cycle. At full power, the phase current is either full on or full off.
I have not seen a controller like that. In fact, I think it would be dangerous. The controllers I have seen, will emit beeping noises and refuse to start the motor at all until the operator has lowered the throttle to full stop first. Some controllers enter the configuration mode if they are switched on with the throttle at max.