There's an access fee set up by the man/family in charge of the land that was 200DKK (around €27) last year, which is quite steep but at least includes a well-maintained trail and basic facilities like a toilet and I think little cafe. The entrance hut may or may not be manned if you go at crazy hours, and you may or may not find a place to drop the cash if no one is there.

As for camping, I'm not sure but I know that the Faroes are generally quite strict as to where you can camp legally. Fishing I believe is permitted, with a permit. Best doing some research.

You can only fish in the lakes if you have a license. You can fish in the sea without restrictions. You can not bring fishing equipment that isn't unopened (to prevent introduction of foreign diseases). Individual people own the different open lands, so you can't just go camping or hiking wherever you'd like. They use the land for their sheep. There's some (read: a lot) specific hiking routes you can hike on without restrictions, and some you have to pay for (the one in OP requires payment for upkeep since it's crazy popular). Hope that clears it up a little bit