Olaf Kyrre is definitely amongst the kings I´d have wanted in the viking/early middle ages. Kind of a quiet type, likes building churches and not going to war.
He´s still going to have to deal with a danish invasion. Sweyn who was fighting Hardrada regularily over Denmark after installing him in Norway made two attempts OTL, Norway´s hold on England is weaker than the Normans would be I assume. Sweyn is probably even more pissed, both Norway and England are a part of his uncle Knut´s empire after all.
Could be, but if the two brothers cooperate anything like OTL, he has to fight England and Norway at the same time, which he might not be keen on.
I could also well imagine the Normans trying again. Olaf Kyrre would need to be a very good king to avoid being deposed, not saying that´s impossible.
Iirc things turned more difficult after 1066. William's ally Baldwin of Flanders died in 1067, and he had increasing issues with the King of France.
Also, if William is killed in an unsuccessful invasion, his son Robert (who seems to have been no great shakes as a ruler) will have to spend ages re-establishing ducal authority, so Olaf gets a breather.
Archbishop Stigand died in 1072. If the King (Harald or Olaf) is smart, he will choose a successor with impeccable credentials - Ealdred of York, maybe, or Wulfstan of Worcester - to keep the Pope onside.
If the Norwegian Kings can hang on into the 1090s, the pressure drops even further when so many Norman (and other) barons go off to join the First Crusade. This makes it much harder to raise the kind of force which Willliam needed to conquer England.