It's an awesome movie. xD "Ten bucks says" is a way of saying "I'm putting ten bucks on the line" or, you're right, "I will bet that" and yes, it is used by many English speakers on occasion. It'd usually be used among friends, as it's a casual way of saying it. "Ten bucks" is not a fixed amount. That number is however much the person is betting. You could say "A million bucks says you will not be able to fit yourself through the eye of a needle" or "Twenty bucks says you won't be able to eat that entire plate of food", something like that. Any amount can be said. It is a way of daring the person to do it. "My money says you can't, and if you can, then you get my money". As for your last question, Fury might not be attempting to be grammatically correct, I wouldn't put it past him, but whenever I've heard it said, it's "(number) bucks says", so I think he's correct there. While you're also right, most plurals would be "say" instead of "says", I think in this case it is not referring to the "bucks" in particular but rather the bill, the piece of money, the item that has been bet, and it therefore used as singular. I'm not too sure of that myself, however, just that I've always heard it using "says". Of course, many native English speakers are grammatically incorrect at times, that could just be our problem. :p As another note, you probably already knew this, but a "buck" is a slang term for a "dollar". Just thought I'd add that in there. :p

Yes, it means "I would bet ten bucks that you're wrong." Americans definitely use it, but the amount isn't fixed. It could be five, ten, twenty, etc., but it's usually a reasonable amount, not a million bucks. Grammatically, I suppose it should be "say" but it is always used with a singular verb. It can be used in British English, except the unit of currency is different, quid or pounds instead of bucks.