Right turn: right suspension compressed, left wheels on the outside have further to travel, if both spinning at the same speed then you will break traction on one side or the other. Not sure what type of differentials are legal in F1, but the technology in the article is plausible in the absence of some fancy limited slip diffs.
You do not want to floor the pedal while still getting out of the corner. The side way force means you have less grip for forward motion, and too much torque to the tires and they will spin.
Isn't that backwards? If you're light on the suspension, that means you have less grip, and thus less traction.