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Which is exactly the position that Scotland is in, vis-a-vis the UK.
Scotland is (part of) the UK. You mean vis-a-vis Westminster, I suspect.
And no, it is not "exactly the position that Scotland is in."
Scotland is not an independent state by most definitions. It does not have representation (in most cases) with international bodies (Breton Woods, UN). It does not have bilateral representation as an equal state with foreign governments. It is not recognized as an independent state by foreign governments.
It is a part of the UK. It's right to independence, although perhaps morally unquestionable, is not legally straight forward (as is the case if a member state wants to leave the EU). It would require Westminster to acknowledge Scotland's independence (as horrible as that sounds). If it tried to unilaterally break off you could, in theory, see civil war break out (think the Basque region).
Only because it says that it is.
Currently, is defers some of its sovereignty, in return for everything being part of a powerful trade bloc, and other advantages (and some disadvantages) provided by being a member of the EU.
It can easily say that it isn't, and there's nothing that Europe can do to prevent them (other than take away the UK's EU-provided toys).