It's likely a setup where the big ring is actually one piece with the spider. Not uncommon on lower end 70s/80s bikes. Still a three piece crank setup.
You could also build a back wheel on a 27" rim. The main problem with riding on 27" wheels is the lessened tire selection. You can generally find 1 1/8 or 1 1/4 width tires easily, but not narrower. You can cut the old hub out of your thrift store fuji and rebuild the wheel around a flip-flop, which is the route I'd take.
The wider tire is not a bad thing, if you're riding in an urban setting. I prefer a slightly wider tire on my fixie, because it's an around-town bike. I ride with a 28.
I would use a front brake if you're riding in an urban setting. There are those who will argue with me on this, but I like a redundant braking system-- ie, if one brake fails, the other can back me up.
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