How long can a limb such as an arm be stuck somewhere such as a rock before it becomes unsalvageable? would there be lasting consequences if the limb was saved before that time and would it be possible to only regain some movement in this case?

Each situation is unique. The most important factor is where the arm is pinned and whether the circulation to that limb is cut off. Without circulation, tissues begin to die. The rate of tissue death is dependent on age, health and many other factors. There is no way to predict whether the limb will regain function after suffering circulation loss without allowing some time to go by.