0: https://manifold.net/doc/mfd8/zip_codes_are_not_areas.htm
They don't represent geography at all, they represent the organizational structure of USPS.
They work by making the address on a letter almost meaningless. For some smaller population zip codes you can practically just put the name and zip code down and achieve delivery.
In other words, is it safe to assume that for entity in a zip code is less than x distance away from the closest entity in the same zip code?
What they do not have is any sort of spatial consistency, they are a convenience for mail sorting. So if you start analyzing patterns across zip codes, you are pulling in information that is likely useless for or harmful to answering your question.