Did St. Peter know St. Paul?

Yes, St. Peter and St. Paul knew each other. Peter said of Paul:

“So also our beloved brother Paul wrote to you according to the wisdom given him, speaking of this as he does in all his letters. There are some things in them hard to understand, which the ignorant and unstable twist to their own destruction, as they do the other scriptures” (2 Pt 3:15-16).

Paul, for his part, usually referred to Peter as Cephas, which is a form of the Aramaic Kepha, the name Jesus gave to Peter (Jn 1:42) and which means “rock.” The most famous confrontation between Peter and Paul is reported by Paul in his letter to the Galatians:

But when Cephas came to Antioch I opposed him to his face, because he stood condemned. For before certain men came from James, he ate with the Gentiles; but when they came he drew back and separated himself, fearing the circumcision party. And with him the rest of the Jews acted insincerely, so that even Barnabas was carried away by their insincerity. But when I saw that they were not straightforward about the truth of the gospel, I said to Cephas before them all, “If you, though a Jew, live like a Gentile and not like a Jew, how can you compel the Gentiles to live like Jews?” (Gal 2:11-14).