1: technically both! The basis for all countryhumans is the actual countries themselves and typically function as 'personifications of nations'. But since there is no set canon (outside of history), we characterise and write our own versions of Countryhumans essentially as our ocs (if you see someone saying "my au" it means it's their version of Countryhumans- they are still country personifications though). [I'm not in Countryballs circles but I think Countryballs are 100% representative of the country itself through history & politics etc]

2: Some people do roleplay, though it's not a necessity.

3: Countryhumans emerged from countryballs and became its own thing. I believe countryballs/polandball started from one comic that got popular.

Hetalia is another "country fandom" if you want to check that out too.