Moon stays in orbit because the gravitational force on it is balanced by the centrifugal force acting on it. Weightlessness means there is no gravity. The Earth's spinning motion causes gravity. 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.