Christ's Church is where two or more are gathered in His name, as Christ said. Christ renamed Simon "Cephas" ("Peter","rock") because Peter announced that Christ was the Son of God and that is the rock of Christianity that the gates of hell cannot not prevail against. Christ's rock is certainly not the Catholic Church. The Catholic Church is one of the aspects of the gates of hell that has always tried to prevail against Christ's Church throughout history...killing martyrs, burning bibles, keeping the people illiterate, taking their money, etc.
Peter never went to Rome. That was Simon Magus, who renamed himself Simon Pater, Pater meaning father ("pope"), to go to Rome imitate Peter after Peter rebuked him in Samaria for trying to buy his way into an apostleship. Magus was just another of Satan's counterfeits, he's had a lot of them throughout history.
No, we’re not doing this here. Start a new thread in the Religion forum, and I’ll tackle all that baloney there.