There are a few Halachas that apply to a Jew's relationship with his country. For example, Dina Dmalchusa, another is not to rebel (although its Halachic strength is disputed, all agree that under normal conditions, one should keep those three oaths.)
What defines a country vis-a-vis these laws?
For example, if there were religious Jews in the United States before the revolution, at what point would the Jews be permitted (or more accurately, obligated) to support the United States? Would Jews be allowed to support the Confederacy? On the other hand, were Jews permitted to join the Union if they came from the south?
On one hand, maybe the Confederacy is considered an independent country invaded by the Union (as they viewed themselves). On the other, maybe the South were rebels, so it would be forbidden to help them.
At which point would Jews be obligated to obey their laws? At which point did "United States law" trump "British law" vis-a-vis Dina Dmalchusa?
A further question (similar to this one):
At which point does a group of people become a country. For example, if one lived in a neighborhood which was run by a Mafia, would he be obligated to obey the laws of that Mafia (for example, if he got away with not paying "protection money", would he still be violating "Dina Dmalchusa")?