First you have the kinematic equation incorrect. It should be
Where s is the position v is the velocity and a is the acceleration.
From what you have given in the problem the acceleration of the ball is due to gravity only
Since the ball is dropped its initial velocity is zero and its final height is zero also. so we get
From here isolate t squared and then take the square root.
for the 2nd part you can just solve again with half of the height to see if its true or not, but before you do that you should try to figure it out based on physical reasoning.