Short answers, pulled from the story.
The name Westminster comes from "Westmynstre", an informal description of the abbey church of St Peter's situated west of the City of London. Until the English Reformation there was also an Eastminster abbey on the other side of the City of London, in the East End.
King Edward the Confessor rebuilt St Peter's Abbey between 1042 and 1052, with the building completed around 1060 and consecrated on the 28th of December 1065. Edward died just a week later on the 5th of January 1066 and was buried in the church.
Westminster has been the home of England's government since about 1200, when the Palace of Westminster became the principal royal residence and the royal treasury was transferred there from Winchester. From 1707 it became the seat of the Government of the United Kingdom.
The Westminster system is the parliamentary model of democratic government that evolved in the United Kingdom and was adopted by many other nations, particularly in the Commonwealth of Nations and former parts of the British Empire.
Westminster became a city in 1539 when Henry VIII's Reformation established a cathedral there. The cathedral and diocesan status lasted only from 1539 to 1556, but the city status remained and was formally confirmed when the Metropolitan Borough of Westminster was created in 1900.
According to legend, a fisherman named Edric ferried a stranger across the Thames to Thorney Island in the early 7th century, and the stranger turned out to be a miraculous appearance of St Peter, who came to consecrate the newly built church. Every year on the 29th of June, St Peter's Day, the Worshipful Company of Fishmongers presents Westminster Abbey with a salmon in memory of this event.