Short answers, pulled from the story.
The Treaty of Saint-Clair-sur-Epte, concluded in 911, was an agreement between Charles III of West Francia and the Viking leader Rollo. Charles granted Rollo lands along the lower Seine in exchange for Rollo's pledge to defend the territory from other Vikings and to convert to Christianity. The exact date of the treaty is unknown, but it is believed to have been concluded in the autumn of 911.
Philip II of France declared Normandy forfeit in 1202 and seized it by force in 1204. English sovereigns continued to claim the mainland territory until the Treaty of Paris in 1259, when they formally ceded that claim. Only the Channel Islands remained under the English Crown.
Rollo was a Viking leader who received lands along the lower Seine from Charles III of West Francia in 911. Whether he was Danish or Norwegian is not known. He had been defeated at the battle of Chartres by Richard of Burgundy and Robert of Neustria earlier in 911, and agreed to convert to Christianity and defend the granted territory from other Vikings.
The Channel Islands are the last remaining part of the former Duchy of Normandy under British rule. When the English Crown relinquished claims to continental Normandy in the Treaty of Paris of 1259, the Channel Islands were retained. The informal title has never been formally abolished. In Guernsey, official documents still title the British monarch "Duke of Normandy," and the loyal toast in the islands is "The Duke of Normandy, our King" rather than simply "The King."
The Bailiwicks of Guernsey and Jersey were created around 1290 by Otto de Grandson, who had been Lord of the Channel Islands since his appointment by Edward I of England in 1277. This division split what remained of the Duchy of Normandy after the mainland portion had been absorbed into France in 1204.
Several Old Norse legal traditions persisted in Norman customary law. A charter of 1050 uses the word ullac, from Old Norse utlagr, for the penalty of banishment. The duke held the droit de varech, from Old Danish vrek, giving him rights over shipwrecks. He also held a monopoly on whale and sturgeon, mirroring Danish law under the Jutlandic law of 1241. Marriage more danico, without a church ceremony, was legally recognised in Normandy, and the first three dukes practiced it.