Regarding the naming of the Yaoguai:
At least some of their family names are the names the animal makes.
Cat Yaoguai's family name Miao = Meow
Cow/Bull Yaoguai's family name Niu = Moo
Snake Yaoguai's family name Shi = Hiss
I'm not sure how far this goes, I'm not sure what sound Turtles make, so I'm not sure how accurate Gru would be, although it sounds right?
Most of them are actually just the literal name of the animal.
'Niu' is actually just 'cow', or perhaps more accurately 'bovine'; linguistic structure of Chinese makes fine-grained distinctions kind of awkward. Similarly, pig(boar) and Zhu, bear and Xiong, turtle and Gui (though it's more commonly used with Wu-), frog and Qin (-wa), tiger and Hu (Lao-), chicken and Ji, snake and She. My guess on rabbit is that they inverted the syllables and used an alternate romanization (Tu-zi to Si-tu).
Not sure what wolves are, and Cat is definitely the onomatopoeia for meow, and not the name of the animal (Mao).
(Note that none of these are really pronounced the way you'd read it in English either; straight off the top, they're all missing the tonal marks which indicate inflection.)
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How are you supposed to deal with a disaster in Mt. South? Based on the info, each sect in the area is supposed to help out with it, getting rewards based on contribution when it finishes... and a big penalty if it's left incomplete. Except your sect is the only one that operates there, and this earthquake event is lasting 20 days, generating 20 brownstone a day, and requires 1000 to safely resolve.