Uh, the Catholic church has gone through a few splits of its own. Much larger, I might add, than any of the Protestant splits.
No. There has always been only One, Holy, Catholic and Apostolic Church. There is only one Pope, and one Catholic Church. Schismatics and heretics have indeed separated from the Church, but not by following the bishop of Rome. The Catholic Church remains always one, no matter how many schismatics and heretics leave her.
-A8