Short answers, pulled from the story.
Reykjavík sits at a latitude of 64 degrees 08 minutes north, making it the northernmost capital of any sovereign state. Nuuk, the capital of Greenland, is slightly further north at 64 degrees 10 minutes, but Greenland is a constituent country rather than an independent state.
The name comes from Old Norse roots meaning "smoke" and "bay", and has been translated as "Bay of Smoke" in English-language travel guides. It was inspired by steam rising from hot springs in the area that Norse settlers would have seen when approaching the coast.
Ingólfr Arnarson, a Norse settler from Norway, established the first permanent settlement at Reykjavík around AD 870, according to the Book of Settlement. He chose the location by casting his high seat pillars overboard and settling where they washed ashore, a decision his slaves located after three years of searching the coast.
Reykjavík is officially considered to have been founded in 1786, when the Danish Crown abolished monopoly trading and granted the settlement an exclusive trading charter. It was the only one of six chartered communities in Iceland to hold onto that charter permanently.
On the 10th of May 1940, four British warships anchored in Reykjavík's harbour and completed an Allied occupation of the city within hours, despite the Icelandic government having declined to consent on grounds of neutrality. The number of foreign soldiers stationed in the city eventually equalled the local population, and the occupation brought significant economic recovery after the Depression years.
All buildings in Reykjavík are heated by geothermal means, drawing on a total thermal capacity of around 830 megawatts from fields within the city and two combined heat and power plants, Nesjavellir and Hellisheiði. Geothermal systems also heat public pools, hot tubs, and snow-melting infrastructure built into streets and pavements in the city centre.