Something not moving can't have any energy. A force acting on an object does work even if the objects does not move. Energy is destroyed in transformations from one type to another. Energy can be recycled. Energy is not related to Newton's laws.
Energy is a force.
Conservation of momentum applies only to collisions. Momentum is the same as force. Moving masses in the absence of gravity do not have momentum. The center of mass of an object must be inside the object. Center of mass is always the same as the center of gravity.