Loss of downforce does not necessarily mean it goes tumbling. Skits basically means it's easier to create the suction that provide the downforce. Loss of that means it lacks the grip it would otherwise have, not that air gets under the car in a way that send it flying. The front wing and rear wing would still produce some downforce that keeps with the wheels on the ground.

Not necessarily, but it does make it more likely; that’s why I wrote “may”. If the design has skirts to generate more downforce, designers will decrease downforce generated elsewhere.

Having said that, I think skirts were forbidden more because they make driving a car through corners too easy and races too dull than out of safety concerns.