I am not going to try to answer all your questions here. I will just try to give a little insight into how AC motor control works.Generally, when a motor spins, it creates a voltage called the back emf (the fact that it is spinning causes it to also act as a generator). When the applied voltage is greater than the generated back emf, the amount of current that flows depends on how much lower than the applied voltage the back emf is. As an unloaded motor speeds up, the back emf increases until it nearly reaches the applied voltage, and the current decreases until it reaches nearly 0 A. A small voltage difference is needed to create the small current needed to overcome losses in the motor. If the motor is then loaded, the speed drops, the voltage difference increases causing the current to increase causing the output torque to increase and supply the needed load torque.In an induction motor, the voltages and currents are sinusoidal AC waveforms which are in sync with the rotation of the motor (if it is a synchronous motor, like one with permanent magnets to provide the field) or slightly lower in frequency than the synchronous speed of the motor (if it is an induction motor). Thus, to control the speed of an induction motor, both the speed and the frequency of the driving voltage must be adjusted together. As speed goes up, both the voltage and frequency must increase and vice versa. Some controllers do this by maintaining a simple V/Hz relationship. Other controllers do this by endeavoring to actively match the "position"of the applied current (and thus field) with the position of the rotor. This is called field-oriented control (FOC).In three-phase motors, it is very easy to control the direction of the applied torque and thus the direction the motor rotates by the way it sequences the currents through the phases. It can start a motor in a very smooth and controlled fashion from a stop, even when loaded. In a single-phase motor, since it lacks other phases, some mechanism is required to get the motor to rotate in the direction desired. You mention a number of these methods in your OP. I can imagine these mechanisms getting in the way of the efforts of a single-phase controller. It's kind of like a 1-cylinder steam engine that can get stuck at top or bottom dead center and no attempt at varying the amplitude or frequency of pressure applied will cause the engine to start to rotate. Some other mechanism is needed to get the engine rotating like a push by hand, an auxiliary motor, etc. A 3-cylinder engine with cranks positioned 120 degrees apart ensures there is always a cylinder in a position to produce torque.If you can first get the 1-phase motor going, you could then control its speed to some degree using above techniques but you certainly would not be able to control it all the way down to zero speed and/or into the reverse direction.Perhaps someone here has more experience with this and could add to the discussion.Hopefully from this discussion you see that using a dimmer will only decrease voltage without changing the frequency and will not work very well.
