Prepare for rain no matter when you may be going. The chance of avoiding rain in Norway on a 3 week bicycle vacation is 1 in a million. It simply never happens. Remember to leave room for plenty of food in your bicycle panniers. You may easily ride 50 kilometers without finding a shop if you are north of the southern-most part of the country.
Bread is fairly inexpensive, whereas vegetables and meats are very expensive.
When in the mountains you may drink water directly from the rivers. Just make sure it is running water. Accomodation Bring a tent. Camping sites in Norway are low-service, and fairly expensive, but in Norway you may pitch your tent anywhere in the woods as long as you do not disturbe people. In principle you should ask for permission from the landowner - but usually you will have no clue as to who owns the land.