Total momentum of the system

Explanation

1. zero
2. zero (because the carts' momenta (plural of momentum!) are in opposite directions)

There is a compressed spring between them, but a rope is holding them together.  Since the carts are in equilibrium, the total force on each of them is zero.  if the rope is cut, however, the compressed spring exerts an unbalanced force on each of the objects.

Since these forces are exerted as long as the spring is in contact with the carts, and since the force is exerted on one cart exactly as long as it is exerted on the other, each cart receives the same impulse.  Recall that impulse is equal to the change in momentum since each cart receives the same impulse, each cart changes its momentum by the same amount.

There is one difference, however.  The forces on the two carts are in opposite directions.  Thus, their impulses are in opposite directions, and the direction of their momentum change is opposite.  This just means that one gains momentum in one direction but the other gains momentum in the opposite direction.