Thanks for the clarification on the second question.
If there have been other high summoners, why aren't they as worshipped as the main four? Braska makes sense, since he was the last one, but why are the other three given pride of place?

Yet another question bugging me too. When the calm rolls round, why don't summoners start their journey then? That way, when the calm ends, Sin has only just returned and a summoner can hit it straight away, with it doing minimal damage to Spira.
My only guess is that it's something to do with the fayth not being active while Yu Yevon is rebuilding Sin, but I don't think that's anything more than a guess on my part.