1) Grimm/Carroll doesn't want real Alice Liddell, but the one he remembers in the past and wrote a book about: Alice's Adventure Underground or Alice in Wonderland. Or should I say that Grimm okay with TCO since he never knew little Alice, but Carroll did.
2) The Alice Grimm/Carroll met first in a Dream was TCO.
3) The Alice Carroll wanted was probably a doll, Alice-02, since she drops her fairy tale if you kill her, but it's just my theory.
4)
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(potentially Mabel) because "This world doesn't need two of the same girl", but Node saved her. Now Alice exists and not exists like a Cheshire Cat, while
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. Though it's just my crazy theory.
Who was a Cheshire Cat in Alice in Wonderland? It was Carroll, the avatar of the creator of the story.
And Cheshire tells you in this game "
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", she could tell about herself in a second or third person. It can all be a dream of Alice...
But that sounds too crazy since there are inconsistences I guess.