Short answers, pulled from the story.
The political union began in 1536 or 1537 when King Christian III united the kingdoms following the Count's Feud. This personal union eventually developed into an integrated state known as Denmark, Norway by modern historians.
Sound Tolls collected from control over the Oresund made up two thirds of Denmark, Norway's state income. Kings such as Christian IV became extremely rich from these revenues generated by the powerful navy enforcing trade through the Baltic Sea.
Under the Treaty of Brömsebro in 1645, Denmark, Norway had to cede Norwegian provinces including Jemtland Herjedalen and Idre & Serna. The conflict concluded with a Swedish victory after seven years of fighting that started with the Northern Seven Years' War.
At its height the empire covered about 2,655,564.76 square kilometers. This vast territory included areas in Northern Europe North America Africa the Caribbean India and the Virgin Islands before settlements were sold to other nations.
King Frederick VI had to cede the Kingdom of Norway to King Charles XIII of Sweden on the 14th of January 1814 at the Treaty of Kiel. A constitutional assembly declared Norwegian independence on the 17th of May 1814 following objections to these treaty terms.