If Scotland does become independent, citizenship of the UK and the shiny new People's Republic of Jockestan will be a massive conundrum.
Will British people living in Scotland lose their UK citizenship & passports, and will people living in England, Wales and Northern Ireland who identify as Scottish through birth or ancestry be able to claim Scottish citizenship?
Maybe I could wear a skirt and self identify as a Scotsman?
My guess is that it'll be similar to when the Irish Republic was formed. Residents were (and still are I believe although things have changed due to the GFA) allowed to self identify as either Irish or British or both. And most countries have grandfather rights too. Britain has very few rules/restrictions on dual citizenship, although I do sometimes get asked if I'm a dual citizen at military sites.
If I could get a EU passport via legitimate means then I would, providing the Socialist republic of Scotland doesn't go all USA on it's citizens demanding world wide taxation.
Maybe, but the world has moved on quite a bit since 1921 and I think public opinion would expect the UK to take a page from the EU's playbook on how to deal with separatists.
I think it would be a good opportunity to scrap the common travel area for example, which would make it easier to deport foreign caravan dwellers who abuse our hospitality and outstay their welcome.
I suppose the nearest equivalent would be the dissolution of Czechoslovakia into the Czech Republic and Slovak Republic in 1992. Wikipedia has a page on it, and says "As of December 31, 1992, citizens of the Czech and Slovak Federal Republic could either choose to become Czech or Slovak citizens." Neither country were EU members at the time, joining in 2004. So yes 1921 was a long time ago - but 1992 isn't.
Dissolving/Reforming the CTA won't happen. Nothing involving Ireland (North or South) can change without the agreement of so many parties that it's just impossible. Reinforcing Hadrians wall could happen, but the major damage will happen to Scotland anyway so why should the rUK bother - they'll implode soon enough anyway without us 'helping'.
The bigger issue for the rUK would be Faslaine. It'll either have to become something like Gibraltar or RAF Akrotiri (UK Sovereign territory), or the whole kit and caboodle would need relocating to somewhere in the south - probably Cornwall/Falmouth - which will be massively expensive although good for the Cornish economy.