That's not too rare. Curved swords do exist. I've learned that from Skyrim. Curved knives are a bit rarer, but they exist. Not counting knives with a curved edge but a straight(ish) spine.
Actually, scabbards were often thrown away in battle if they weren't worn.
Her excitement is cute.
"Shouldn't you consider making a bit more profit?"
Since there's no tsuka-ito, the wrapping of the handle, this makes it more of a hwando (Korean version of katana) than a proper japanese katana. Correct me if I'm wrong, I'm just using weeb stock knowledge.