Knowing that there will not be perfect conservation of linear momentum in any experimental condition (most notably due to the presence and impact of friction), if there were no frictional forces present is it expected for linear momentum (theoretically speaking) to be conserved during each of the cases being analyzed.
Linear momentum should be expected for cases 1-3, since they are all elastic collisions but not for case 4 since it is a perfectly inelastic collision.
Linear momentum should be expected for all cases since momentum is conserved in all collisions.
Linear momentum is not expected in any case since momentum is not conserved in any collision.
Linear momentum is expected in case 4 since it is a perfectly inelastic collision, but not for cases 1 - 3 since these are elastic collisions.
Experimental Cases
two carts, each without spring-loaded bumper; one moving, one initially at rest
two carts, each without spring-loaded bumper; both moving, approaching each other
one cart (without spring-loaded bumper) approaching a cart (with spring-loaded bumper, spring fully extended); cart without bumper moving, cart with bumper initially at rest
one cart (without spring-loaded bumper) approaching a cart (with spring-loaded bumper, spring compressed); cart without bumper moving, cart with bumper initially at rest