[Can't find the real daycare couple]

After you defeat the tangrowth in obsidia, there will be a girl in onyx (the building next to the casino iirc) asking you to check the daycare couple, whom are acting weird, because they’re fake. Go defeat the fake couple, and then you can find the key to the warehouse in the small house at obsidia park.

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Abomasnow 

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Arboliva 

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Espathra 

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Tympole

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Nacli 

[Name change (I'm sorry I didn't know where to post this)]

Well there’s no in-game ‘legal’ way, but you can change it using the debug mod. Just go to the mod market and look it up.

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Noivern 

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Koraidon 

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Trumbeak

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Ralts

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Ursaring

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oranguru

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fuecoco

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Rockruff

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Yamper

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Smoliv 

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Yveltal

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Entei 

[Help Z-Crystal]

Which z-crystal to be exact? If you mean the z-ring (that allows you to use z-moves if a mon is holding a z-crystal), it’s obtainable after the 13th badge. More on this here.

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Xurkitree

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Naganadel

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Umbreon 

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Onix 

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Sprigatito