A push account is defined by Inno as :
"This is defined as unbalanced routine resource (resources, Knowledge Points, etc.) transfers from one account to the next even if involved accounts do not belong to the same player." So technically all those baby cities that are dependent upon bigger cities to climb the spire or tournament every single week, would be push cities. Inno wont tell us exactly where they have drawn the push line, but it is out there, somewhere.
Farm cities would be most of my cities. I have diamond farms, cities on multiple worlds that spire and craft for the sole purpose of earning diamonds that I only spend in my main city. So they are diamond farms.
I have never heard of a "ghost" city before.