Balls 1 and 2 are each thrown horizontally from the same height above level ground, but balls 2 has a great initial velocity after leaving the thrower's hand. If air resistance is negligible, how do the accelerations of the balls and the times it takes them to hit the ground compare?

Both horizontal accelerations are zero. Both vertical accelerations are equal . . . the acceleration of gravity. They fall for the same length of time. If thrown at the same time, then they hit the ground at the same time. A bullet shot from a high powered rifle and one dropped from the muzzle at the same time hit the ground at the same time.

They have the same acceleration, which is the acceleration due to gravity. This is because they accelerate only in the y-direction, there is no acceleration in the x-direction.They hit the ground at the same time because they have the same initial y-velocity, distance, and acceleration.