I'm not sure what you mean by 'why', but it's a consequence of momentum conservation. If a ball with momentum +mv collides elastically with a fixed wall and thus rebounds with momentum -mv, the wall (and all attached to it) must end up with an total momentum of +2mv.Any one can tell me why the momentum of the wall is 2mv while a ball collides it?
Of course it is conserved.Are you suggesting that momentum is not conserved during the collision?
I think you are a little confused here. The velocity of the ball after striking the wall IS different! (Speed is the same, but velocity is a vector quantity so a change in direction is a change in velocity)Of course it is conserved.
When ball hits the wall, the wall does not move because it is held at bottom and due to rigidity and elasticity of the material. The wall gives this back to the ball as reaction due to the action. That's why the velocity is same as it was when the ball was striking it. The wall doesn't have it's own momentum which it is imparted to the ball(it seems you suggested that), if so was true then velocity of the ball after striking would be different. That's what conservation of momentum is.... final momentum equals initial
there is no such thing as a stationary body. if the house is firmly stuck to the ground, the earth gets the extra momentum 2mv.wall is not moving.. a stationary body does not posses momentum.
When the ball strikes with +p momentum the wall gives out equal and opposite reaction of -p momentum.