How does Gemini have Lucy's keys? When Lucy fights Angel for the first time, Gemini turns into her and has duplicates of her keys. That makes no sense, because there's only supposed to be one of every key. They even say so in that fight?

If Gemini can make duplicate keys, could Lucy hypothetically summon the Spirit King with all of her keys and then just use the Gemini copies afterwards?
Gemini has the power to copy things. So since Gemini can copy the keys doesn't mean that lucy would be able to use them. Duplicating doesn't mean to copy. Copying something like on a printer isn't the real design. It's a "copy" of the real thing. Meaning that she wouldn't be able to use the copy, but she would be able to use the duplicate. Saying that Gemini only uses copies not duplicates. So lucy would not be able to use the fake keys.