do suspension systems have to be compatible?
YES! The correct suspension system is essential.
Not usually. With the computer design systems the manufacturers use, the suspension is 'tuned' to the car the type of market the car is aimed at. Moving a suspension to another car could lead to a bad ride maybe even a safety problem if the suspension is not designed for the weight of the new car. Even inside the same car model line, the suspensions can vary between a model met for a sporty ride to a family hauler.
they certainly need to have space enough and the proper mounting points. you certainly couldnt fit the leaf spring suspension most trucks have on the rear axle into a little honda civic, even if you actually wanted to. even when talking the same setup, coil over vs coil over, there is length of suspension, both max and minimum for full travel, and weight capacity. take the honda civic suspension and put it in a full sized truck, 4x4 with even more suspension travel, and if the weight doesnt destroy the suspension the movement range will.