Short answers, pulled from the story.
Nazi Germany needed to control the port of Narvik because it was the only year-round outlet for vital iron ore supplies from Sweden when the Baltic Sea froze over in winter. Without this route, German steel production would have stalled completely due to the natural barrier blocking most shipping routes.
British destroyers HMS Cossack intercepted the German auxiliary ship Altmark near the Jøssingfjord and freed all 299 prisoners taken from Allied ships sunk by the German cruiser Graf Spee. Seven German sailors died during the hand-to-hand combat before the British boarding parties secured the release of the prisoners.
Adolf Hitler officially approved Operation Weserübung on the 1st of March 1940 after General Nikolaus von Falkenhorst took command of planning on the 21st of February 1940. The coordinated invasion launched at 04:15 Norwegian time on the 9th of April 1940 targeting six primary locations including Narvik and Trondheim.
The cruiser Blücher sank after being struck by 40-year-old torpedoes launched from land-based tubes at Oscarsborg Fortress, delaying the main German invasion force for over 24 hours. Despite this resistance in the Oslofjord, the capital fell less than 12 hours later through airborne troops.
Captain Bernard Warburton-Lee led eight British destroyers to sink two German ships during the First Battle of Narvik on the 10th of April before his flagship HMS Hardy was destroyed. The Second Battle began on the 13th of April when Warspite entered the Vestfjord and four British destroyers chased fleeing vessels until all German crews abandoned their ships by 18:30 local time.
Organized Norwegian military resistance ceased on the 5th of May with capitulations at Hegra and Vinjesvingen after Allied leadership decided to withdraw forces by the 28th of April. This failure directly caused the Norway Debate which resulted in Prime Minister Neville Chamberlain's resignation and Winston Churchill taking office.