Did Peter ever meet Paul in person?
Yes. Gal 1:18: “Then after three years I went up to Jerusalem to visit Cephas, and remained with him fifteen days.”
Cephas comes from the Aramaic word for “rock” which is what Peter means.
Gal 2:11 also records a meeting between the two where they had a disagreement.
I am not sure why this would be questionable according to scripture, but it sure does make me wonder if Paul was inspired to write more because of Peter.
*The Council at Jerusalem
15 Then certain individuals came down from Judea and were teaching the brothers, “Unless you are circumcised according to the custom of Moses, you cannot be saved.” 2 And after Paul and Barnabas had no small dissension and debate with them, Paul and Barnabas and some of the others were appointed to go up to Jerusalem to discuss this question with the apostles and the elders. 3 So they were sent on their way by the church, and as they passed through both Phoenicia and Samaria, they reported the conversion of the Gentiles, and brought great joy to all the believers.[a] 4 When they came to Jerusalem, they were welcomed by the church and the apostles and the elders, and they reported all that God had done with them. 5 But some believers who belonged to the sect of the Pharisees stood up and said, “It is necessary for them to be circumcised and ordered to keep the law of Moses.”
6 The apostles and the elders met together to consider this matter. 7 After there had been much debate, Peter stood up and said to them, “My brothers,** you know that in the early days God made a choice among you, that I should be the one through whom the Gentiles would hear the message of the good news and become believers. 8 And God, who knows the human heart, testified to them by giving them the Holy Spirit, just as he did to us; 9 and in cleansing their hearts by faith he has made no distinction between them and us. 10 Now therefore why are you putting God to the test by placing on the neck of the disciples a yoke that neither our ancestors nor we have been able to bear? 11 On the contrary, we believe that we will be saved through the grace of the Lord Jesus, just as they will.”**
Nearly identical to the tale in Galatians.
As for the two saints influencing each other. Both got their Gospels directly for Christ, as all the Apostles did. Paul describes his revelation in that first part of Galatians.
Despite vigorous claiming his Gospel came from no man, on specific issues, like circumcision of Gentile-Christians, Paul went to Jerusalem to consult with Peter and as the account in Acts describes, Peter listened to both sides and agreed with Paul. If you keep reading Acts, James the Just, first bishop of Jerusalem chimes in too in favor of Paul.
Paul also mentions is Galatians that he took the time to speak with the Apostles in Jerusalem to confirm he was preaching the true Gospel.
Then after fourteen years I went up again to Jerusalem with Barnabas, taking Titus along with me. 2 I went up in response to a revelation. Then I laid before them (though only in a private meeting with the acknowledged leaders) the gospel that I proclaim among the Gentiles, in order to make sure that I was not running, or had not run, in vain.
So it was sort of like today, in that the Church leaders met with each other to discuss any questions and disputes they may have had, and that Peter had a primate role is deciding these disputes.*
Make that got their Gospels directly FROM Christ.