Engine Braking - keeping it in gear without throttle. You're dissipating energy by compressing air.
For hard braking, that's probably the case... I'm not familiar with it being excluded to hard braking only....
Sharp corners.... Simply explained (and ignoring any other loss), the power necessary to turn to is inversely proportional to the radius of the turn. Bigger turn = less power. If you want me to get more into the physics, just let me know