About the changing direction, due to the 'English' on the ball.
Suppose that the ping pong ball is rotating clockwise around a vertical axis, as it travels to the other side of the table. The drag on the right side of the ball will be less than on the left. As its rotation rate decreases (due to higher friction on the left-hand side), the ball will curve to the right, in order to conserve angular momentum.
If the game was played on the moon, which has negligible atmosphere, the ball would not curve to the right.