Its speed is increasing, as it falls. The ball is accelerating. Objects accelerate when forces act on them. Pushing or pulling on an object can make it change its speed or direction. Pushing or pulling with the same force on a less massive object has a greater effect than pushing or pulling on a more massive object.
Force is a vector.
Pushing forward will make the object accelerate forward. It will change its component of the velocity in the forward direction. If it initially at rest, it will start moving in the forward direction. If it is already moving in the forward direction, its speed will increases with time. If it is initially moving in the backward direction, its speed in the backward direction will decrease.