Baby bella, crimini, portabello, all the same species. Call them Crimini, sounds more exotic.
I don't have a grinder for my KA so I don't know how fast the auger will turn but I would think you should be able to run it at damn near full speed. Don't worry about burning it up with a few pounds of chicken.
I use a dedicated grinder and have put 30-40lbs at a time through it when making sausage, it won't break a sweat.