Hi Christian, most of this information is found on the Need to Know or Route pages.
The Fjord Norway page is here: http://www.cyclenorway.com/routes/norse-all-road-series/overview/fjord-norway/fjord-norway/

a) The prevailing winds are south-easterly, meaning, in general, there is more tailwind heading north.
But you’re going through the mountains that will sometimes shelter the wind.

b) I don’t think anyone can answer that question. Maybe the Strava heatmap can give you a clue about which way cyclists go? But as far as I’m aware, there is no preferred direction.

C) If you had two different routes, we could compare which is more flexible. But the Fjord Norway route is pretty straightforward, with little opportunity to deviate.

D) All the mountain passes are clear of snow by mid-June. The only one to double-check is Gamle Strynefjellsvegen, which usually opens on the 15th of June.
http://www.cyclenorway.com/opening-closure-of-roads/

In either direction, you will get both tough and easier sides of the mountains to climb. There is not much difference in either direction. If you go North-South, there is 14100m and South North 14500m. Four hundred meters over 800km is very little difference.

If you go over Aurlandsfjellet to Lærdal, you can take the bus through the two long tunnels to Sogndal (or vice versa). I think there are two a day, and if you time it right, it should be a simple procedure.

If I was you, I would start in Oppdal and end at the famous Flåm microbrewery, drinking their famous IPA! That’s a good way to celebrate your achievements! You can also go up to Myrdal and take a train to Opsete and continue riding to Bergen if you want to extend the trip. See the Oslo to Bergen route.