Concerning your quotes about Peter and "the Rock":
The Rock is Peter, insofar as he maintains his confession of Christ, who is the True and Original Rock. If the faith gets tossed, so does St. Peter's status as Rock. The Pope of Rome threw the Faith out with, among other things, the filioque and created grace, so he's no longer a viable successor to St. Peter. The Patriarch of Antioch, however--who was put in place by St. Peter before the Bishop of Rome was--still is.
I ran into a couple of interesting quotes on this recently...
"Upon this firmness, He says, I shall raise My Temple, and it will rise upon the steadfastness of this faith, and the loftiness of My Church will mingle with the heavens. The gates of Hades shall not master this profession..."St. Pope Leo
"Thou art Peter, and upon this Rock from which thou didst receive thy name, that is, upon Me Myself, I will build My Church. Upon this perfection of faith which thou didst confess I will build My Church, and if anyone turns aside from the society of this confession, even though it may seem to him that he does great things, he will not belong to the building which is My Church."
I found it very interesting that St. Leo and St. Bede, both of whom were, by the standards of their times, big supporters of the papacy, should have interpreted the "Rock" as the confession of faith rather than as St. Peter himself. Even St. Cyprian, who interpreted the passage in exactly the way the modern RC's do, still saw it as only supporting the authority of each bishop, rather than that of one overarching bishop. He said, "The authority of the bishops forms a unity, of which each holds his part in its totality."