Yes, for instance the UK would probably fare very differently if London (which can itself feel like a foreign country to non-Londoners in the UK) was removed and the country's wealth re-evaluated.
This is true of basically any country except very rich, tiny countries like Singapore or the UAE.
Na. GDP pp is meaningless without accounting for inequality and civil liberties.
Sure but we're talking about urban/rural disparities in the same country. PPP and civil liberties are generally pretty similar there.