I dont think anyone will do the whole thing for you, perhaps you should attack the parts you know and ask about the others.
I'll offer this, there are many types of AC motors. In many cases, the easiest way to change their speed is to alter the frequency of the applied AC. Its sometimes called variable frequency drive.
As for the hall effect sensor, it seems that your is outputting a voltage which depends on the proximity of a magnet which is probably mechanically coupled to the pedal somehow. To get these working together, you just need some interface circuitry. Perhaps a micro which reads an ADC from your pedal sensor and controls the frequency of a PWM system.