Theseus' ship? Isn't that "Umvolkung" nonsense again? Philosophy, political sciences, and law have have rummaged about these questions for the last few centuries and have developed some pretty good answers. Of course, they are mostly not simple and all too long and intricate for this forum, but I guess you can pick up any modern book on theory of the state to get your answers.
But I get the distinct notion that you have a certain idea what a country, state, or nation is, considering the conflation with culture, and it is not very embracing of pluralism. I'd wager you'd like Schmidt, maybe Zippelius, but not Böckenförde.