A lot of questions there, brother, and I'm no expert. But I'll do my best(and no doubt will be ripped apart by people who actually know what they're talking about:redface
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Scots, Irish and Welsh are all, gentically speaking, pretty much identical. Yes, they are all Celtic. The Picts are a bit of a mystery, mainly because they left no written record(or at least none that anyone has been able to decipher so far). They were the original inhabitants of Scotland. The name Picti or Pict is actually a Roman term and means "Painted Ones" - the Picts used to paint themselves with blue tribal markings.
The Picts were no match in open battle for the professional Roman Army. Unfortunately for the Romans, after the first battle, which the Romans won easily, the Picts learned their lesson. They used their intimate knowledge of the land, combined with superior one-on-one fighting skills(the Roman Legions were only world-beaters when they could work and fight as a team)to slaughter thousands of Legionaires in guerilla warfare. According to legend, the entire Ninth Legion, approx 4 - 5,000 strong, was wiped out to the last man by the Picts. Although even professional historians have yet to agree as to what actually happend.
Eventually, sick of losing men in a country that had precious few natural resources, the Romans built two BFO walls and declared that this was the final border of the Empire. Scotland was never completely conquered by Rome.
The Picts were eventually defeated about the 9th Century AD by Irish settlers. One of their Kings married a Pictish princess and the two groups gradually merged, forming the basis of what eventually become the Scottish race. Many Scots, including myself, still carry Pictish DNA.
Although it is of course entirely fictional, one of the Conan novels has a wonderful and probably very accurate discription of the real Picts:
"Conan had borne a blade against the howling Pictish hordes, and deeply respected their battle-prowess. Not even the mighty warriors of the frozen North, in their berserker madness, could long stand against the inhuman ferocity of the Picts..."
The Norse(Viking simply means "to go raiding")had a huge impact on Scotland. The Norwegians conquered and held the northern Islands of Scotland for hundreds of years. Eventually they were defeated by Sommerled, Lord of the Isles. Sommerled himself was half-Norse, and was the ancestor of a racial group know as the Norse-Gaels; people with both Scottish and Viking ancestry. Today, almost 500,000 people can trace their lineage back to Sommerled. This is the second largest group of people in the world who are descended from a single ancestor. Only Ghenghis Khan has more descendants.
Past my bedtime. If anyone is still interested, I'll post more tomorrow.