Honestly, it's an odd question the way you've framed it.

Assuming basic veracity of early Christian documents, Peter emerges as the leader of the Jerusalem church very early on, from the mid 30s, and is apparently the most prominent of Jesus' disciples. Jerusalem is the main staging-base for Christian expansion within Judea, and Acts portrays Peter as giving "apostolic agreement" to missionary enterprises among Samaritans and Gentiles.

Peter seems to largely disappear from the main narrative in Acts sometime in the 50s, and Jesus' brother Jacob (James) takes the leading role. Late 1st/early 2nd century sources are virtually unanimous in placing Peter in Rome, and depending on how you consider the authenticity and social setting of the letter 1 Peter, engaged in writing to believers from Rome now in northern Asia Minor. Most early traditions put Peter's death in Rome during 65-68 under Nero.

All of which would attest to Peter being a significant leader of the early church. However it seems from the later half of Acts and from Galatians that Peter's main focus was ministry among ethnic Jews, while it was left to Paul to specifically engage mostly Gentiles.

As for your second question, I am not really sure how you even formulated it. Peter, a 1st century Jew from Galilee, purported to have spent 3 years living with Jesus, would feel most at home in a meeting of Jesus. The Catholic Mass is a religious tradition that developed over centuries in cultural and linguistic contexts very distinct from Peter's. Would Peter agree with it? That's a theological question. Would he feel like it was familiar? No, because that's anachronistic - the form of the mass you likely have in mind is at least several hundred years later than Peter's lifetime.