How do you avoid - you know - not killing each other by accident?
There's rigorous training, tests etc. you have to pass the tests with the combat trainers at controlled sessions called "Battle Practice" before you can fight tin a real show/battle.
You're pulling blows? Blunting weapons?
Yes, pulled blows, blunted weapons, you taught to not hit certain locations like groin, head, centre of the back, knee, elbows and so on.
Basically anything that can't take a hit.
I imagine that if things get heated or competitive you might not pull your blow as much as you should?
It happens, but then when it does, depending on the severity, it could be as simple as an apology and being told off to offending person or as much as to be thrown out of the society with a life ban.
I've never seen anyone killed or anything like that, but if that did happen I'd imagine the police would get involved. But in the 15 odd years I did it for I never saw that happen.
The worst I've seen is someone got shot in the eye with a rubber tipped arrow. He lost his eye.
It's also worth noting that one/some of the game designers of Legend based the on a recreation of re-enactment combat (I.E. they are Re-enactors themselves.)
Does that even exist? Competitive reenactment?
Yes it does. mainly I've done competitive re-enactment of the Viking period. Although sometimes we get hired to to Scripted battles as well.