Short answers, pulled from the story.
The Denmark-Norway union began in 1536-1537, when Christian III united the two kingdoms and imposed Lutheranism as the state religion. It ended on the 14th of January 1814 with the Treaty of Kiel, which ceded Norway to Sweden.
Denmark-Norway held colonies in West Africa (the Gold Coast), India (including Tranquebar and Serampore), and the Caribbean (the Danish West Indies, centered on the Virgin Islands). It also held Greenland, the Faroe Islands, and Iceland as Norwegian overseas possessions.
The Sound Tolls were taxes levied on ships passing through the Oresund strait. They made up two thirds of Denmark-Norway's state income and financed the wars and building projects of kings such as Christian IV.
Denmark-Norway became an absolutist state in 1660, when the Rigsraad was abolished. The change was formalized in the Leges regiae, signed on the 14th of November 1665, which declared all power to rest in the hands of the king, who was answerable only to God.
The Danish West Indies, centered on the Virgin Islands, remained a Danish colony after the 1814 dissolution. Denmark sold the territory to the United States in 1917, and it became the U.S. Virgin Islands.
Norway was industrialized from the 16th century and built a strong export economy in shipping, timber, and mining, making it an economic equal of Denmark. Historians have noted that Norway was one of the world's wealthier countries throughout the period of union, and that Norwegian farmers were on average more prosperous than Danish farmers.