I have two questions:
Bat speed in cricket is the velocity that a batter can achieve with his customized slab of English willow, But i believe there is no standard of how to measure it has been accepted.
It is largely the television channels that measure the speed of bat and it is from the video their cameras capture. Its mostly the speed of swing from stationary position to hitting the ball position.
The nature of pitch surely affects the pace of ball. A dry dusty pitch and a very damp pitch is slower because the ball grips and holds to the surface more. A skiddy kind of pitch with a little moisture will have a slight increase in pace due lower value of coefficient of friction. The difference in pace caused by difference in the texture of the pitch is less than 5mph.