Short answers, pulled from the story.
Norse influence began in the late 8th century when Viking longships reached Hordaland from Shetland within twenty-four hours. This period established the Northern Isles as the closest parts of Scotland to Norway and the first region to experience Norse culture.
King Olav Tryggvasson Christianized the Northern Isles in 995 by summoning jarl Sigurd the Stout to accept baptism under threat of death or destruction. Bishop Henry of Lund was appointed prior to 1035 to oversee the new religious order following these events.
Pagan practices are evidenced by grave goods found on Colonsay and Westray though confirmation remains elusive. Odinic beliefs persist only through the Odin Stone possibly derived from an oathing stone rather than active worship.
The Treaty of Perth signed in 1266 yielded rights to Hebrides, Mann, and all claims to the Kingdom of Scotland after a stalemate at the Battle of Largs. Haakon Haakonarson led an ill-fated invasion resulting in this transfer of power from Norway to Scotland.
Shetland remained part of Norway until its mid-15th century transfer following the pledge of Orkney as security against dowry payment in 1468. Christian I pledged both regions while money was never paid making the connection with the crown of Scotland perpetual.