Short answers, pulled from the story.
The Normans were a people who arose in the medieval Duchy of Normandy from the intermingling of Norse Viking settlers and the local population of West Francia. Their origins trace to the treaty of Saint-Clair-sur-Epte in 911, when the Viking leader Rollo swore fealty to King Charles III of West Francia in exchange for coastal lands along the English Channel.
The Norman conquest of England began with William the Conqueror's decisive victory at the Battle of Hastings on the 14th of October 1066. The invading Normans and their descendants largely replaced the Anglo-Saxons as the ruling class and introduced the feudal land system formalized in the Domesday Book in 1086.
The Kingdom of Sicily was established after Norman forces under Robert Guiscard and his brother Roger the Great Count captured Sicily and Malta from Muslim rulers. Roger's son, Roger II of Sicily, was crowned king in 1130 by Antipope Anacletus II. The kingdom lasted until 1194, when it passed to the House of Hohenstaufen through marriage.
Bohemond of Taranto and his nephew Tancred joined the First Crusade in 1096 with an army of Italo-Normans. Bohemond became the de facto leader of the Crusade through Asia Minor and founded the Principality of Antioch after the successful siege of the city in 1097. Norman mercenaries had also been fighting in Byzantine service in the Near East since at least the 1050s.
The Anglo-Norman language, which developed after the 1066 conquest, was eventually absorbed into the Old English spoken by the Norman settlers' subjects. Together with earlier Norse and Latin influences, this shaped the development of Middle English, which in turn evolved into Modern English. The Normans also introduced words into Welsh, such as baron (barwn).
Norman customary law, developed between the 10th and 13th centuries, survives in the legal systems of Jersey and Guernsey in the Channel Islands. The musical notation system of denoting notes by letters, developed at Fecamp Abbey in the 11th century under abbots William of Volpiano and John of Ravenna, remains the most common form of pitch representation in English- and German-speaking countries.