What are the circumstances in which any can be used with a singular and with a plural?
- Do you have any car?
- Do you have any cars?
For example, commenters have indicated both
You cannot use any with a countable singular. You can use it with a plural, or with a mass noun — “do you have any milk,” for example.’
"You don't have a Ford. You don't have a VW. You don't have a Chrysler. Do you have any car?" is perfectly reasonable.
Clearly the rules are quite complex.