Is it possible for a lever to change from one class to another during its rotation (e.g. it starts out as a third class lever and ends as a first class lever)?
Yes. All that is required is for the load, the fulcrum, or the force to change position. For example, if the load were to climb along the lever arm of a class 1 until it passed the fulcrum, the rig would then become a class 2. In the same manner, the leverage ratio can change at any time.