No, BH209 does not work well in 12 gauge shotguns. It MIGHT be worth trying it in a 20 gauge, but it's really meant for moderate bore rifles like 40 to 54 caliber rifles with stouter loads. You can give it a try if you want, but I got bloopers in a shotgun.
Chokes, if for turkey, go ahead an use the tightest you want. There is a practical limit to choke where your pattern stops improving, but its way up there like .060"-.070" constriction. All of what you listed will work fine, and I doubt you will notice much difference between them besides usual shot to shot variation. I'm assuming all 3 are extended, but if not, I would avoid flush chokes for the one reason you will want to remove the tube to load each shot.
