1: "Strictly speaking of course there will be only one new country."

Yes Scotland

2: "Scotland has a long history as an independent country."

Yes that is right it's last spell as an independent country lasted from about 1357 to 1707, after which it retained its religion, law and right to print bank notes as part of Great Britain.

3: "The "country" consisting of England, Wales and part of Ulster, whatever it chooses to call itself, has never previously existed at any time.

The country which has contained all three has existed since 1801 and it was called the United Kingdom, it will remain being known as such.

4: "On what grounds is it claimed that it is not every bit as much, at the very least, a "new country" as an independent Scotland would be?

Well Kevin just niggling little things like membership of the EU, NATO, a permanent seat on the Security Council of the United Nations and various other international agreements.