I've live with, bred, trained, and run American Pitbull Terriers all of my life. To my mind a Staffordshire (Bull) Terrier is a, 'little pussy'. Personally, I would never waste the life or physical wellbeing of a Pitbull I'd spent two or three years training on, 'backwoods critters'. That's NOT what I bred and trained Pitbulls for.
Neither would I ever, 'bait' one of my Bulldogs just for the Hell of it. In 1990 one of my Pit Bulldogs actually save my life during a home invasion. During the hundreds of hours I'd spent training that animal I never thought I'd ever actually need him for anything other than occasionally, 'showing off'. Then, one quiet Sunday morning it suddenly happened!
Here's the answers, as I know them, to your questions:
30 lb male Raccoon - Not if the coon can get to water.
30 lb Male European badger - I don't know?
35 lb Male coyote - Some coyotes, yes. Others I've encountered, no.
40 lb Bob cat - Unless you're, 'running' the cat, it ain't ever going to happen.
50 lb Beaver - I've seen 35 - 40# beavers, but never a 50# one. Beavers are very peaceful creatures that never stray too far from water. Somehow I don't see this as a problem.
35 lb Nutria rat (Coypu) - I don't know?
35 lb Wolverine - Again I don't know; but, I strongly doubt it.
40 lb Javelina - If the dog can get a good neck hold, maybe.