So whether an object moves or not, it has some form of energy. If it has KE, then with respect to the frame of reference in which its KE is measured, it also has momentum. In the popular sense, conserving energy means not wasting energy. In the physics sense energy conservation refers to a law of nature that underlies natural processes. Nor can it be created.
Energy is transferred or transformed, without gain or loss.
That's what a physicist means in saying energy is conserved. If the ball is given an initial KE, it will return to its starting position with that KE and hit the instructor. Work is defined as the component of force in the direction of motion multiplied by the distance moved. When the direction of the force is perpendicular to the velocity, there is no force component in the direction of motion and the work is zero. The string tension is everywhere perpendicular to the bob's direction of motion, which means there is no component of tension along the bob's path, and therefore no work done by the tension.