"Do you have green shoes?"
Translation:Czy wy macie zielone buty?
Well, "mieć" will never take Nominative. It may just be that the Accusative form is identical to Nominative, but it's Accusative nevertheless.
The notion of being animate is only important in one situation: when you need Accusative of a masculine singular noun. For example "I have a brother" = "Mam brata" (Accusative looks like Genitive) vs "I have a shoe" = "Mam but" (Accusative looks like Nominative).
Here, you have 'not masculine-personal plural' (anything that is not 'a group of people with at least one man') - and for this gender, the Accusative form is identical to Nominative.
Not sure if it was a typo (of singular 'pani') or a grammatical mistake, but "panie" is plural (ladies), so it's "Czy panie mają zielone buty?". The second sentence is correct.
So it's "Czy [pan/pani] ma zielone buty?" (Do you have green shoes, [sir/ma'am]?) and "Czy [panowie/panie/państwo] mają zielone buty?" (Do you have green shoes, [gentlemen/ladies/mixed group]?).
In Formal You, it's common and natural (in my opinion, even more natural) to put the verb before the subject, so to have "Czy ma [pan/pani]..."/Czy mają [panowie/panie/państwo...". That's probably the only context in which it's safe to put the verb before the subject.