Short answers, pulled from the story.
The Faroe Islands became part of Denmark following the Peace of Kiel in 1814, which dissolved the union of Denmark-Norway. Before that, the islands had been part of the dual Denmark-Norway kingdom since 1380.
Grímr Kamban is identified in two medieval sagas, the Flateyjarbók and the Saga of Óláfr Tryggvason, as the first Viking to settle the Faroe Islands. His surname Kamban is of Gaelic origin, suggesting he may have been of mixed Norse and Irish descent, a so-called Norse-Gael.
Operation Valentine was the British pre-emptive invasion and occupation of the Faroe Islands after Nazi Germany occupied Denmark. Britain acted to prevent Germany from using the islands as a strategic base in the Battle of the Atlantic; the British instead built an airbase on Vágar, which still operates today as Vágar Airport.
The Faroe Islands were granted home rule in 1948 with the signing of the Home Rule Act of the Faroe Islands. A 1946 independence referendum had produced a majority in favour of full independence, but Denmark refused to recognise the result.
A collapse in fish stocks, caused by overfishing with high-tech equipment, combined with massive government overspending drove the crisis. National debt reached 9.4 billion Danish krones, the national bank called in receivers in October 1992, and unemployment in Tórshavn rose to 20 percent. Denmark provided a bailout that eventually totalled 1.8 billion DKK.
The name derives from the Old Norse fár, meaning livestock, giving fær-øer, which translates as sheep islands. The name first appears in written records on the Hereford Mappa Mundi of 1280, where the islands are labelled farei.