Two questions and a small confusion that is not letting me do my homework:

When is said that an object is rotating it is mandatory that the addition of rotational momentums gives 0?

Under what conditions, two forces of same magnitude but different direction exerted in a body, would make it rotate?

If there is no moment (torque) then there is no change of angular momentum [ I omega = constant]

If they are not opposite in direction through the same point, they cause a moment, called a "couple"