A) Since the dart hits the hanging mass and sticks to it, the time of interaction is equal for both bodies. According to Newton's second law, the force caused by the dart on the block is the same as the force caused by block on the dart. Therefore, the impulse is equal for both objects.
B) The block and the dart would reach higher height. According to energy conservation, calculate the height H:
We see that the height is directly proportional to the speed of the dart. Therefore, higher speed would cause the block and the dart go higher.