We have explained how the ride height influences the grip: it's just that the "lever arm" you have on the CoG varies. You can read this:
http://phors.locost7.info/phors01.htm
Or watch this image we've posted a couple of times, you have to read the texts in the order of the numbers.
The same effect applies if you look at the car rolling laterally: you shift the weight. The outer wheel will have a lesser weight, thus less friction. The lower the CoG, the lower the weight transfer. So, a car with a higher CoG brakes and turns worse just because the friction on its wheels is "unbalanced".
On a regular car you can brake so hard as to have zero weight on the rear wheels, thus in an emergency braking you brake only with the front wheels.
I've seen braking marks on the pavement where the rear wheels's streaks are "interrupted" because of this: the rear of the car "jumps" in the air, so you brake ony with the front wheels.
Simple:
if you lower the CoG your car will brake in a smaller distance, even if you use the same brakes, tyres, car, driver, etc.
Same goes for turning: you can turn so hard as to "devoid" the outer wheels of weight, thus you take away all the friction from them.
Sorry if you already knew this, but until you understand it you cannot race in a proper way, perhaps someone will find it interesting.