We use our vang as a preventer going downhill and to keep the sail from losing air in lighter winds and bigger seas. Never heard the one about it being used to keep the boom parallel to the horizon. A topping lift can put a belly in the sail in light airs going off the wind as can our outhaul with our RF mast.
Again off the wind, I can let the traveler out downwind for a better angle of pull, and less sheet.
Sorry, I can't help with the backstay thing cause I've never used one, but bending a mast intentionally kinda sends shivers up and down my spine.