> What do these folks do for work that they can live up in the Arctic in this fashion?
The name of the island in the article is a link to its Wikipedia page, from which another link takes you to the page for Nordland, the county it belongs to. https://en.wikipedia.org/wiki/Nordland#Economy
> How do they keep the dome's light from being completely obliterated.
As another poster noted, the dome is not very well isolated. As a wild guess, this might mean that thin layers of snow could melt off if it's not too cold outside.
Also, during the three winter months when it doesn't get light outside at all, you might as well live under a layer of snow. Its reflection of the house's lights should give an overall brighter feeling than if the light just goes off into the arctic night.