Be honest, do you really think you'd be given ALL the oil and gas money for the north sea? National waters extend a few miles offshore, beyond that its fair game (well it would be if nations hadnt agreed already who got what area). Seeing as those treaties were written up as great britain/uk/whatever, the English would have as much claim to (whats left of) the oil and gas as you.
That's factually not true, unfortunately. Ownership/jurisdiction over all the oilfields is settled in legislation and agreements in tedious detail going back decades. There wouldn't be a free for all if Scotland left the UK and there are numerous models for dissolution of assets in previous countries/federations dissolving. It's not legal rocket science.
It's wishful thinking, of course, that Scots would be relaxing in a jacuzzi of oil money as soon as independence came around.
What currency would an independent Scotland choose?
The groat,
obviously. Actually, it could be anything: could continue to use the pouund sterling (!), a new Scottish pound, use the Euro (don't have to join the ECB), use the dollar, use the Swiss franc, use whatever is convenient. There are quite a few countries that don't have their own currencies and use their neighbours' (none are superpowers, I concede, but neither is Scotland): Montenegro, Kosovo, Andorra, Monaco, Liberia, Panama.
If Scotland becomes independent, will Scots in the UK become "illegal immigrants"?
No - most likely at the time of independence the model would be that Scots living in the rest of the UK would be entitled to keep their UK citizenship or acquire Scottish citizenship, and anyone who's currently a UK citizen in Scotland would be allowed to acquire Scottish citizenship. (Don't believe it's likely that in either case acquisition would result in loss of UK citizenship - it's up to HMG but traditionally they haven't been big on cancelling citizenship en masse).
No-one with the slightest credibility is suggesting Scotland would be outside the EU so Scottish citizens would be entitled to live in the UK on that basis (assuming they weren't put on the Polish/Bulgarian accession country scheme, which would be amusing!). But probably in any case in parallel to the EU stuff you would have a UK/Scottish deal on the UK/Irish model anyway - unrestricted immigration, open borders, no discrimination between citizens A and B, service in each other's miitaries allowed, full voting rights...