It's all complete RNG. I had to kill Vaal 87 times to get both of it's crowns, but it took me less than 10 for Teostra. The others were around the 15-35 range.
As for the events, same thing. You are just at the mercy of RNG despite the increased chances. It's still certainly a lot better than investigations. You can save yourself more time by knowing what you need and then return from quest after slaying/capturing the monster.
Ex) If you just need Great Girros large, just go straight for it. If it looks huge then attack and if not then abandon quest > return to camp to restart the quest. Once you think it's a large Girros then kill it and then return from quest to see if it was a crown. No need to fight all the others.