what should be the power factor of a generator connected to national grid in order to have maximum stability? Whether it should be high or low?

If you define maximum stability as the torque required to pull the rotor out of step with respect to the stator (a pole slip), then the maximum stability would be a condition where the rotor excitation is high with respect to the torque applied to the shaft. Thus, a synchronous machine will be more stable in the over excited state when the field current is high. For a generator, this would be a lagging power factor and for a motor it would be a leading power factor.

well, it depends on your local agency or local code...