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You have a lot of issues here, but let me see if I can help. First of all, at minimum you have a verbal contract that has been fully executed. The fact that your fiancé did not sigh the document gives you a credible claim that you did not accept it terms. Further, refusing to sell him a kitty unless he agreed to buy vitamins from them too would be an illegal tying contract (forcing you to buy something you don't want to get something you do).
With respect to the fleas and ear mites issue, you can either deal with it, or give the kitty back, but not both. I'd be happy t review the "contract", but for it to be enforceable against you, it would need to be signed by you. Outside of that she is out of luck.
Lastly, if she cannot or will not produce the paperwork documenting the cat is what she says it is, you can return it.
I hope this helps. Hollar if I can do more.