Answer
Yes. Yes. Twice as great.
Work Step by Step
Yes, when you throw the ball, you exert an impulse on it to provide the change in momentum. This also applies when you catch the ball moving at the same speed. You change the ball's momentum by the same amount in both cases, i.e., the impulse is the same.
If you catch the ball and then throw it back again at the same speed, the change in momentum is mv - (-mv) = 2mv, twice as great than if you merely stop the ball. Thus, it requires twice as much impulse.
