If for every action there is an equal but opposite reaction, then why doesn't a ball keep on moving when made to move between two surfaces, should elasticity of surface, gravity and friction be mentioned in this theory?
You are talking about Newton's first law, i.e, inertia (ball should keep moving)
This has absolutely nothing to do with the current group-theory tag.
The first law doesn't need to explicitly mention friction, it already says "when no force is applied". It's upto you to keep track of external forces.
The answer is that there is friction. Friction is a dissipative force, meaning that friction will cause energy losses. This causes the ball to stop rolling: in a vacuum that would not happen! These things can be taken into account when doing calculations.
I think Sir Issac Newton's laws works fine here.
Object will continue to be in rest or move in straight line until a external force applied on it.
the ball starts/stops moving only when an external force applied on it.
The ball uses the force 'F' applied on it to move in acceleration 'a' on direction of force.
Every action has an equal and opposite reaction
the ball is stopped if an equal force applied on opposite direction of ball's movement.
But usually it stops due to friction/gravity/other obstructions which does not come into action exact opposite direction or exact force needed to stop ball. so it will move as long the above condition satisfies. also the friction reacts on exact force and direction opposite to ball's movement (same for all the obstructions ) and when these forces sums upto the force 'F' which used to made the ball move, ball will be stopped !