"Self Appointed" prob. not the most accurate description for the concept - the Pope is indeed elected by the Cardinals - it would have been clearer for me to opine the Church has appointed itself and it's clergy as the representatives of God on earth.
Boreas, all you wrote is accurate - I tend to supply condensed versions on message boards, as I find the majority of users do not relish longer posts.
It is refreshing to see when someone formulates a thoughtful reply.