How is air conditioner room unit fan motor controlled?
How did the original controller (that was in AC internal unit) control
  motor’s speed? Did it use resistors to lower voltage, changes
  frequency or used some electronics called TRIAC?


Speed can be controlled by changing the capacitor value or by inserting a series resistor. Three-speed fan motors often work by switching capacitor values. Series resistors could be used, but the resistors dissipate heat and that method is not easier or less expensive to implement. For speed adjustment over a continuous range, electronic voltage reduction using a triac or some other switching device is used to provide electronic voltage reduction. That method works well for controlling fan speed because less torque is needed to operate a fan at lower speeds. That somewhat compensates for increased motor losses, so the motor does not overheat.

See also:

Speed control for PSC induction motor

Speed control on a ceiling fan induction motor

Varying run capacitor for speed control of single phase motor