Short answers, pulled from the story.
Norse-controlled territories in Scotland included the Northern Isles of Orkney and Shetland, the Hebrides, the islands of the Firth of Clyde, and associated mainland areas including Caithness and Sutherland. At the height of Thorfinn Sigurdsson's rule in the 11th century, permanent Scandinavian holdings amounted to between a fifth and a quarter of the land area of modern Scotland.
Scandinavian Scotland spanned from the 8th to the 15th centuries. Viking influence began in the late 8th century, and the period formally closed in the mid-15th century when Orkney and Shetland were transferred to Scottish rule; Orkney was pledged to Scotland in 1468 when Christian I of Norway used it as security for an unpaid dowry.
The Orkneyinga Saga is the principal Norse source for the history of Scandinavian Scotland. It was written in the early 13th century by an unknown Icelander and provides much of what is known about the earls of Orkney and Norse activity in the region, though it is sometimes contradictory when compared with Irish and English annals.
Norse settlement produced a near-total replacement of pre-existing place names with Norse ones across much of the Northern and Western Isles. Norn, a local form of Old Norse, was widely spoken in Orkney and Shetland well into recorded history, and Norse may have survived as a spoken language in the Outer Hebrides until the 16th century. Pictish place name evidence in Shetland is virtually non-existent, with only three island names, Fetlar, Unst, and Yell, as exceptions.
Norse raids initially weakened Pictland, Strathclyde, and Dál Riata, but those harassed kingdoms eventually united into the kingdom of Alba, the nucleus of modern Scotland. Norse aggression thus played a significant role in pushing the Gaelic and Pictish populations toward political unification, just as Viking pressure in the south helped Wessex expand into the kingdom of England.
Norwegian control over the Western Isles ended with the 1266 Treaty of Perth, following Haakon Haakonarson's ill-fated invasion and the stalemate of the Battle of Largs. Under that treaty, the Hebrides, Mann, and all rights the Norwegian crown "had of old therein" were yielded to the Kingdom of Scotland.