Civilization – In Civ 5 vanilla, If some city states enter permanent war, is diplomatic victory impossible

If you kill quite a number of units of a city state and/or keep trespassing on their territory enough to get your score very very low over an extended period of time, they eventually will be convinced that you are so evil it's not worth considering peaceful coexistence, so they will be in perpetual war with you. You will not be able to buy their friendship and relations will not heal by themselves over time.

Actually that doesn't mean too much, though. If you go near them, they'll attack you, and if you leave cities undefended near them, they'll capture those. Apart from that, they won't hunt you across the map and they won't make others hate you as well. If you just leave them alone now and make their area taboo to your units you can still get along with the other city states just fine.

You might choose to have one perpetual warring city-state next to your army outfitter because city-state units train your troops longer than barbarians do.

All cities remember only the original civ that built them. It's much more cost-efficient in the long run to raze cities and resettle in the same place with your own settler given the oftentime nigh untenable cost of the courthouse building (and the fact that it can't be purchased).