Short answers, pulled from the story.
The first known settlers of the Faroe Islands were Gaelic hermits and monks who arrived in the 6th century. These early arrivals lived as religious figures on the remote islands before any Norse presence existed.
Y chromosomes tracing male descent are 87% Scandinavian while mitochondrial DNA tracing female descent is 84% Celtic. The majority of Faroese people carry Scandinavian male ancestry mixed with significant Celtic female ancestry.
The Icelandic Færeyinga saga was written sometime around 1200 and explains events taking place approximately 300 years prior. Historians have understood since the time of the Færeyinga saga that the Viking Grímur Kamban was the first settler in the Faroes.
Most Faroese are citizens of the Kingdom of Denmark where the Faroe Islands are a constituent nation. Citizens participate in Danish elections but also vote for their own parliament which serves as the legislative body for internal governance.
About 21,000 Faroese live in neighbouring countries such as Denmark Iceland and Norway. These populations represent those who moved away from the home islands for work or education.