Yes, the 33's would likely fit. But since you're running 32's now and are happy with them in both fit and performance, I would not hesitate to stick with that size.
Glad they still even make that old size!
Your "stock" gearing could actually be 4.11 already, since that was a factory option. Most did come with the 3.50's mentioned, but being a '77 you likely also have an automatic transmission, which makes the transition with slightly larger tires less of an issue around town. Which might be why the 32's feel alright now.
The 8" wide wheels will be fine with either size, but are as wide as you'd want to go on an 11.50 wide tire. If you thought a 12.50 looks square, you should see an 11.50 on a ten!
The 8" wheels are a better choice in many cases even for the wider 12.50" tires on a Bronco. And are well within the safe range, but some places (large chains mostly) won't mount that combination unless it's on that particular tire manufacturers recommended list. With BFG having changed their sizes a few years ago, they likely list an 8.5 to 10 inch range. Or maybe even a 9" to 10" range.
With that backspacing/offset setup though, the wheels will still fit like wider wheels in the fender. Kind of giving the false impression of a wider wheel, but without the shape of the tire changing. You're still going to notice a difference if you have 7" wide wheels now. But it's still a good combination. I run mine on 7" wheels and prefer that. But 8's look good too.
The '77 needs the clearance at the steering knuckle/arm, but the 3.44" backspacing specified in your list should work fine. I believe most wheels up to about 3.625" backspacing will fit the steering arms on a '76 or a '77.
At 108mm the center bore should be (I think?) about 4.25" or so? For those with good conversion-fu, is that correct? If so that should be more than big enough. 'Ya gotta watch out for those pesky center bores these days!
I can't see the info, but it looks like the lug holes use a standard taper. Problem is you can't trust pics sometimes because they might show a generic version. But if that's correct then your old lug nuts should work as long as they were for a similar style.
Center caps can be very wheel specific, but lots of brands fit different brands of wheels too. So i don't have an answer for you there. You could measure your existing ones and see if they'd be close.
I prefer no caps myself, but with modern wheels the caps often do look pretty good.
Up to you if you want new ones or not. Just because they are not listed as coming with them, does not mean you can't purchase them from the wheel company separately.
I did not look too closely, but your choice does not seem out of line. Sorry you have to go through all the hoops of shipping overseas, and wondering if you made the right choice. Or worse yet, getting them there only to find out they don't fit!
And speaking of that, I would definitely NOT go with the larger tires in your case. Your rear flares are of the early style with the more vertical leading edge. This means a little less tire clearance and a chance you could rub the flare and it's nice paint.
Great looking Bronco by the way!
Paul