And I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it.Again, that is the future tense. Even according to Matthew, written half a century later, the 'church' (ekklesia) doesn't exist when he says that to Peter. It is not "and on this rock I am building my church" or "on this rock I have built my church". And that's assuming Matthew has it right. There's no mention of it in any of the other gospels. That's pretty incredible an oversight - you'd think that would have been a major event in Jesus' ministry. Paul doesn't mention that Peter's the rock of the church. He waits three years to even visit Peter after his conversion via a personal divine revelation.
I'm not sure on your question there? Which church survived? The Eastern Orthodox? The Roman Catholic? The Coptic? Arianism? Nestorianism? Gnosticism?
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@Secret Slave Class - the Essenes and the Dead Sea Scrolls?