Front splitter might make the steering feel heavier but is unlikely to improve stability - in fact it's very likely to make it worse. It will reduce front end lift and increase rear end lift, both of which will tend to make the car less stable.
I think same, if front splitter is mounted, also rear splitter should be mounted! This is a must also for Porsches, if a rear is mounted a front must be mounted to keep car in weight balance at high speeds.