Holy shit this is gonna be a BIG answer... but I'll try!
Do they have any sense of style? Regardless of the answer do they believe they have a sense of style?
In varying degrees! Li-Ming is an artist and while he dresses more casually (and wears paint stained clothes a lot) he does have a sort of cozy style he sticks to. Goose wears the most eclectic shit, like a full properly tailored 3 piece suit. With boots shaped like goose feet. He has to maintain brand recognition.
Lizhi, on the other hand, is very into fashion. She'll try any style at least once after enough time and research! She doesn't have a set style (though she has a set rule of matching her outfit to her jobs), but I guess overall she wears what would be considered light and calming colors unless it's a Gothic style for the day, sticking to pastels and natural colors when possible.
Do they learn from their mistakes?
Not Li-Ming. Holy shit, no.
Who, if anyone, would they trust with their deepest secrets?
Li-Ming and Goose trust each other. Lizhi only trusts herself until something happens later in her story and then it's Mei.
Do they plan in advance or just wing it?
Li-Ming tries to plan in advance, but 3/10 times lately something goes wrong.
Lizhi plans enough to have a rough outline that is flexible enough to work around it.
Goose, true to his birdly name, wings the fuck out of everything.