There are two fast modern submarine cables connecting the faroe islands:
https://en.wikipedia.org/wiki/FARICE-1
https://en.wikipedia.org/wiki/SHEFA-2
Prices of one of the major ISPs: https://www.ft.fo/ver/breidband/
50/10 - 487 dkk, 65.42 euro, 76.29 usd
75/10 - 497 dkk, 66.76 euro, 77.86 usd
100/20 - 527 dkk, 70.79 euro, 82.56 usd
And the other: https://hey.fo/internet/heimanet/breidband/
For comparison, this is about 50% higher than the same services cost from the major ISPs in Denmark.
Although where there's fibre to a large apartment building, it can be half the typical rate.
What about on island connectivity, mainly wireless, or are your lines (especially on the remote islands) good enough for DSL?