Define the origin to be at ground level and up to be the positive direction. Let the position be called s, velocity v and acceleration a.

We have a = -9.81 m/s/s due to gravity.

equation 1.

equation 2.

Now when the ball is at its highest it is neither going up nor down, that is v=0. So set equation 2 equal to zero and solve it for t, the time at which the height is maximum. Substitute this value of t into equation 1 to find the maximum height.

For the second part set equation 1 equal to zero and solve for t, the time at which the ball hits the ground. Substitute this into equation 2 to find the velocity when the ball hits the ground. Since we defined the positive direction to be up, the answer will be negative.

For your second question , v_0 is not known. Use equation 2 with t=3 to find v_0, then you can find the required answer using equation 1 by solving for the only unknown (t).