@magerette: The parliament votes over a confidence/loss of confidence proposal.
Ragarding the formation of the cabinet. What happens after the major election is this:
1. If the party/coalition forming the cabinet remains in majority, the cabinet continues.
2. If the current cabinet loose the majority party leaders will negotiate to see if they can establish a major coalition. Political parties in Norway usually form two blocks: the socialist block and the non socialist bløock. Sometimes the parties in the olitical centre form their own block. Currently a coalition of the two socialist parties and one party in the centre forms a majority coalition.
Based on these negotiations the president of the parliament goes to the king and suggests who he should ask to form a new cabinet, that one will be the new prime minister. The prime minister then select the members of his cabinet. Even if the king can act on his own when selecting a new prime minister, this has not happened in the last 80 years. (It happened in the thirties, when the king contacted the leader of the socialist party which was the major party in the parliament, despite being adviced otherwise. This action meant a lot and did affect the attitude towards the monarchy in the socialist party).
It's not always possible to form a majority government, in that case a prime minister most likely to form a viable minority cabinet is selected.
After formation of the cabinet, the prime minister will present to the parliament an outline on what the cabinet plans to do. Sometimes this results in a loss of confidence vote.
Neither the prime minister nor the members of his cabinet must be a member of the parliament, but I can't think of any case where the prime minister was not. However, when appointed, all cabinet members in the parliament will leave the parliament, to be replaced by a substitute.