The original question was - what happens to English people living in Scotland and vice versa, should Scotland separate from the UK. As someone to whom this very much applies, I have yet to find any answers.
The issues of EU membership, Schengen, CTA and the SNP's proposed open-door immigration policy are likely to make this very complicated indeed.
However, I must correct some incorrect assumptions above.
Great Britain was created by the Union of Scotland and England/Wales. Not the UK - it was created when Ireland joined. So Scotland's spearation would mean an end to Great Britain (the political entity though, not the geographical island) but not the UK. Until such time as Northern Ireland were to leave, the UK would still exist - its subtitle may have to be modified to "of England, Wales and Northern Ireland" though.
You need to understand the concept of successor states. What is very clear is that the successor state to the UK would be the UK. This is not in dispute. A good example of successor states would be Russia from the Soviet Union.
Scotland would be a newly-created nation state. New states not only have to apply for EU membership, but have to be accepted by all existing member states. The current UK membership cannot be retained by two states. The current membership of the EU, the UN, NATO, etc would be retained by the successor state.
New member states also have to sign up to the Euro. The reason that this does not apply to the UK is that it has the opt-out, which is not available to new member states.
The EU Treaty and the EU Commission have made this clear, although it contradicts what the SNP has said.
We cannot assume that the rules would be any different just because a) it is "our" country and b) because a domestic political party says so. At the very least the process would require lengthy negotiations. Of course the SNP suggests everything would be automatically continued because they want people to vote in their favour. It simply is not the case in reality, however.
SO, supposing Scotland does negotiate a membership with the EU. The issue of immigration would be extremely complicated, given the UK government's strict immigration control and the SNP's proposed mass-immigration. The UK is in a CTA with Ireland, but not within Schengen. If Scotland were to sign up to Schengen, this would necessitate very strict border controls between Scotland and the UK.
The SNP has proposed some sort of dual nationality but this has not been discussed with the Home Office. In theory it would allow Scots to retain UK citizenship (a benefit, as Scotland would have no embassies and consulates worldwide) while taking the new Scottish passport. In practice, it would only work if it were reciprocated, and a Scottish passport were offered to any English, Welsh or N. Irish who wanted one.
As someone who has lived their entire adult life in England, but was born in Scotland, I do not wish for my place of birth to cause me problems remaining where I live. I certainly do not wish to become a foreigner in my own country and the prospect of long border control queues at Gretna every time I want to take my son to see his grandparents is abhorent.
All the more so for the undeniable fact that this is all completely unneccessary in the current UK.
The second point is the currency. However Scotland were to join the EU - by negotiation or application, it would be obliged to join the Euro. The timescale is not clear and it may be able to wait until the Euro is favourable.
We must not forget that until very recently, the SNP were stating that Scotland must join the Euro because the Pound was a terrible prospect. Nobody can blame them from a U-turn on the Euro under current circumstances, but there is no getting away from the fact that the Pound is the second choice at best. The Bank of England would be its central bank - in a foreign country rather than a domestic one as present, and Scotland would not have any say in the fiscal controls.
At any rate, I must return to the original question. If anyone here has any proper knowledge of constitutional and/or immigration law, it would be very helpful.
People born in Scotland but now living in other parts of the UK - would they be able to retain UK (English/Welsh/N.Irish) citizenship?
People born in England, Wales or Northern Ireland but living in Scotland - would they also have a choice?