If I win on the attack and conquer, does this happen before or after I score? Before or after conquer effects?

Draven’s ability will trigger and resolve before you gain your regular point for scoring the battlefield and before any conquer effects are triggered. This means that you can’t win from 6 points by conquering a battlefield with Draven without having scored all other battlefields—you’ll gain your point from Draven, then the game will see that you’re at 7 points and give you a card draw instead of a point for conquering.