If the motor is a 1phase/split phase motor, then you will have to reverse the start windings for reverse direction, this type of motor will have a capacitor feeding the start winding.
They do not however, make even close servo motors.
In some cases, a synchronous motor is used that resembles a stepper motor, but runs off 110vac, on these you could theoretically change the frequency for speed control.
The encoder strips usually use the same method as a rotary quadrature encoder, two detected pulses 90deg spaced.
Al.
CNC, Mechatronics Integration and Custom Machine Design
“Logic will get you from A to B. Imagination will take you everywhere.”
Albert E.