"but there are a few glaciers around, so I guess any advice on camping on glaciers would be great as well"
What? Camping on glacier in Finnmark!!! HELLOOOOO
I have lived in Finnmark for nearly 20 years, and near the biggest glacier Øksfjordjøkelen, but it is not a place you go to camp unless you have 1: extensive course in how to move on glaciers. 2: Ice axes, ropes and crampons for glaciers. 3: Special equipment in forms of tents, mats, bags and stoves that could be used in winter camping.
Finnmark has just 3 "big" glaciers, Øksfjordjøkelen (41km2), Seilandsjøkelen (14km2) and Langfjordjøkelen (8km2) They all are in remote areas and hard to get at. Forget the glaciers!
The main part of Finnmark is the flat plateau called Finnmarks-vidda. It is a vast area where the vegetation is mosly low birches. Vidda has also large areas of wetlands, and hence LOTS of insects if you are there in the right time (end june, mid july). Insect repellant is a must, lots of it!
Finnmark is greater than Denmark, but has only about 75000 inhabitants, so there is a lot of places to camp. Since camping is free in Norway on unfarmed land (+ a few rules) you have enough places to camp. Just use google map and the street view, there you may see the terrain.
The sami and their reindeers are dominant in the county, remember to avoid conflict with their culture. Finnmarkseiendommen http://en.wikipedia.org/wiki/Finnmark_Act is the owner on behalf of the state of the land. Look at www.fefo.no for info about licenses for fishing inland. Fishing in the sea is free for all.