Most of Norway's wealth is definitely not owned by the government, where do you get this from? It's mostly owned by corporation's and the people. Statoil and some other large companies are partly owned by the government, but there are many wholly owned privat oil companies competing with them.
No it does not. There are treatments that are deemed to expensive and will not be provided. Typically it will be a trade off between how effective the treatment is and how expensive it is. European healtcare systems does not have infinite money.