Asynchronous motor joule loss calculation
If you know only the input power, output power, voltage, current and rotor resistance, you can not calculate the total joule loss. You can calculate the total losses, but that includes joule losses plus iron losses plus mechanical losses plus stray load losses. Output power is the power transmitted to the rotor minus rotor joule losses minus mechanical losses. I assume that input power is Pa. I assume g is slip and g = (synchronous speed minus operating speed) divided by synchronous speed. The relationships that you state seem to be correct. In some circumstances, you might neglect some losses, but I don't think that it is reasonable to assume that you should neglect everything except rotor joule losses. You could assume some typical relationship among the losses, but that doesn't seem very reasonable either. Are you sure that you have stated everything that you know about this problem?

Edit 1

The stator and rotor leakage (series) reactances are apparently null in comparison to the resistance, and the resistance of the magnetizing reactance is also very small. That means that you can assume that the reactive component of the input current flows only through the magnetizing reactance and the real component is current in one phase of the rotor. The equivalent circuit sets the ratio of stator to rotor winding turns at 1:1 and adjusts the rotor resistance accordingly. Since the motor is wound-rotor rather than squirrel-cage, the rotor resistance is high even with the rings short-circuited.