The Queen is also Queen if various other countries, such as Canada and Australia. We don't generally refer to all these as part of the United Kingdom. THe position in regard to Scotland would be essentially the same.

"Great Britain" is a geographical term for the island, and this will of course continue to be the case. However to be strictly accurate, the country "Great Britain" only existed between 1707 and 1801.

So far as the presence of the Union Flag on the flags of various other nations, I would think that, if they didn't decide on a redesign dropping the flag, they might be likely to hang on to the historic design rather than switch to one involving a new version. After all, joining the USA didn't cause Hawaii to drop the flag from it's own state ensign, seeing it as having a historical significance rather than any political meaning.