Now this part isn't in the Bible, so any Catholics here are more than welcome to correct me. It's believed that St. Peter was the bishop of Rome, thus the placement of the Vatican. The Vatican itself isn't considered any more sacred than any other Church, but it is the location of the head of the Church, and every other Church must answer to the doctrine made there, thus the whole communion wafer dilemna.
No. Peter didn't ascend through the ranks. To my knowledge he was just made pope. And the Vatican itself isn't the authority, it's the position of Pope that hones all the power there.
