Only one force acts on one object. Can the object have 0 acceleration? Can it have 0 velocity?

If force has some finite magnitude then, acceleration can't be equal to 0. But, if does not have any relation with velocity. It can or cannot be Zero.

F = ma

If there is only one force acting on an object, the acceleration cannot be 0, by definition. In order for acceleration to be 0, there would have to be another force opposing the first one ... in which case, there would no longer just be one force acting on the object.

However, the velocity certainly can be zero. Think of throwing a rock straight up in the air. As soon as it leaves your hand, the only force acting on it is the force due to gravity (ignoring any air drag effects). When the rock reaches its maximum height, its velocity is 0 for a very brief moment before it starts to fall back down.