Which informations do I need to calculate the efficiency and horsepower of a 3 phase induction motor?
As far as I know the magnetic force is responsible for the motor rotation. So, horsepower of the motor is mostly related to magnetic flux on the coils (windings). Also magnetic flux is directly related to inductance (Number of turns) and the current flow on the coil. Am I right so far?


That is not quite right. Energy is force X distance. Power is the rate of energy transfer or conversion, force x distance / time. The power delivered by a motor is torque X speed. Torque is force multiplied by the radius at which the force is applied.


  1- What is magnetizing reactance of the winding?


The magnetizing reactance is the part of the stator reactance that produces useful magnetic flux. Due to limitations of the geometry of the motor structure, less than 100% of the winding flux actually contributes to producing torque and transferring energy to the rotor. Therefore the winding is shown in the equivalent circuit as two components. X1 is just an impedance to the flow of current that does not directly contribute to the function of the motor. The flux in Xm is the flux that produces torque.


  2- Why do we want high power factor?


High power factor means the minimum current to deliver a given power to the load.


  3- How can I calculate the horsepower and the efficiency of my motor?


You completely analyze the equivalent circuit. The mechanical power developed in the rotor is the power in R2x(1-s)/s. In the rotor circuit, R2/s is comprised of two parts, R2, the rotor resistance, and R2x(1-s)/s the representation of the mechanism of conversion of electrical power to mechanical power.

You also need to consider that some of the power developed in the rotor is lost to friction and windage rather than delivered to an external load.

Note that you have asked at least four questions. A complete answer would require a chapter in a text book assuming that you have mastered the prerequisites for the course.