Some new points here, and some not so new.

Whilst it is true that 'Good King James'* coined both of the terms 'Great Britain' and the 'United Kingdom', they didn't come into serious use until much later, and not even with the union of parliaments, but only when most of the British Empire was gone, so that it became necessary to have terms to cover British possessions near at hand, other than simply as part of the Empire.

Not only that, but the modern usage is different from that which Good King James intended. He meant the same thing by both Great Britain and the United Kingdom, simply all the areas of which he was king. However, in Modern usage, and officially, Great Britain, aka Britain, means England, Wales and Scotland, i.e. the contiguous British mainland, whereas the United Kingdom or UK is all the above plus Northern Ireland, the Isle of Man and the Channel Islands, i.e. including all the bits directly offshore that are under British rule.

Sadly, even many British people get this terminology mixed up, so it's no great wonder that Americans invariably get it wrong. I used the term 'contiguous' intentionally, as it may particularly help Americans to think of Britain as analogous to the 'lower 48', whereas the whole country is the UK. Unfortunately, even if you get it right, you may come across some drunk in a pub who still tells you that you are wrong, LOL!

As for the kilt not being Irish national dress, it is true on the one hand that it has never been recognised by the Irish government. On the other hand, the main thrust for it's adoption as such was by the Gaelic League during it's early years, and that organisation was founded in 1893, some 19 years before there was any Irish government that could have considered the matter and rendered a decision one way or the other.

Prominent early wearers of the Irish solid green or solid saffron kilt in the late 1800s and early 1900s were invariably Irish nationalists, which to many would be reason enough to wear a kilt as a symbol or Ireland. The concept is hardly new (unless to you anything a mere century old is brand new) and not likely to go away no matter how much some would like to wish it away.

As to whether the English are celts, the oldest known inhabitants of England were the Britons, who of course were Brythonic Celts by definition. To what extent the Angles and Saxons actually displaced them is not really a settled question. It was once thought that they were all driven into Wales or killed, but opinion seems to be softening on that, so the English may be some mixture of Celtic and Germanic (Angle in the North and Saxon in the South), and perhaps Norman, although it has long been thought that the Normans only married into the aristocracy and did not mix with the common people.

Of course, even if the English may have some Brythonic celtic blood, what the English are certainly not is Goidelic celts, unlike the Irish and the Scots. Unless of course, like me, you have both English and Irish blood, for example.

*I prefer to call him that, because in full he was King James II of England and King James VI of Scotland.