No, the residency rule is quite complicated and it is something like ten years plus a different connection as well. I don't know the full details but I'm sure someone else will!
Whilst the peoples are intermingled to a great degree (and it will probably become even more so) there is still quite a differentiation between the peoples. For example, the numbers of English that have moved to Scotland, Wales or Ireland is relatively few, but the reverse is not the case, because the money has generally speaking been in England. That is why the Scots, Welsh and Irish are often seen to have a more distinctive culture than the English - the English are much more of a melting pot. Even so, most people do not have the choice as the cross-breeding goes back too far in history, it's just a significant minority who do.
For that reason there is a healthy anti-Englishness (it's rarely genuine antipathy, just a hope that the English will get stuffed in any sporting endeavour, principally because England is bigger, more populous and has historically been the dominant force) in the British Isles anyway, which allows a number of people to proclaim their ancestry from other parts of the British Isles even if they are actually English.
As far as the parentage rules are concerned, you must have at least one grandparent who was born in the other country. It is not as straightforward as you might think, and certainly the Welsh and Scots rugby union teams have been caught out selecting players with no connection whatsoever.
On the whole it works, there are rarely problems; although us English are extremely miffed that Ryan Giggs chose to represent Wales rather than England. It still comes back to the emotive issue of who you feel you should represent. The Celtic nations are extremely patriotic and that often goes down the lineage of a particular person, even if they weren't born there. The English on the other hand are less vocal, but there are an awful lot more of us, and so the issue tends not to arise.
She's as nervous as a very small nun at a penguin shoot.