Yes, scotland, england and the EU aren't members of the UN (though the EU may be getting special representation there) England is thus not a 'nation'.
More importantly it is not a nation by the standards of international mail delivery. (whoever or however they happen to be)
Also further to the difference between in Northern Ireland and the Republic of Ireland (other than one being an independent republic) if you live in the North (or any other part of the UK) you probably refer to the Republic as 'the South' or Southern Ireland; but if you live in the Republic you almost always refer to it as Ireland, and rarely as 'the Republic' if you need to distinguish between the state and the island... (though the Republic only abandoned it's territorial claims to the North in 1998, with the Good Friday Agreement, which effectively saw the end of the troubles)
Also Ulster refers to one of the four provinces of Ireland (the island) whi h includes all of Northern Ireland (and it's six counties) along with three counties in the Republic (Cavan, Donegal and Monaghan)
Still, if you want to be English and NOT part of the UK then i'm sure there are some english republicans who want to get rid of the monarchy and establish a seperate English parliment. You'd probably be considered a successor state, and thus inherit the UK's permanent seat on the UN security council, and any other international obligations which the UK currently undertakes.
Fortunately for anyone with a Scottish vs English issue, there is an example of Ireland's breaking with the Union to follow. Currently as an EU citizen i would be entitled to vote in local and EU elections in any EU state i was residing. But as an Irish citizen, when i am resident in the UK i get to vote in national elections aswell (but not referenda) and vica-versa.
Keeping this relationship as it is, but extending it to Scotland (should it vote for independance) means that citizenship should be virtually no problem for engaging with democracy.
But the really important question is, what will the UK be if Scotland leaves? The United Kingdom of England, Wales and Northern Ireland? Or The United Kingdom of Southern Britian and Northern Ireland??
EN-GB will remain the common language localisation option, and UK the abbrv of the nation (and postal code) while .uk remains the www TLD. scotland may have some trouble as .sc is the seychelles, .sd is Sudan, .sl is sierra leone. They might want to consider renaming the country (for marketting purposes) .ab is free if Alba was the desired name...