no, a suspension fork does nothing at all to the handling of a bike when compared to a rigid fork
Untrue. If you put too long of a fork it will change the geometry and cause the bike to turn slower but make it more stable at speed. Also, the right suspension fork will keep the tire on the ground over the rough stuff causing it to track better through turns. It will also make your rides smoother and less fatigue on the hands.
Negitive aspects, it will be heavier and cause you to use more energy when climbing unless you get one with lock out.
Slainte