The decision was already made at the Jerusalem council to let go of the dietetic law. That was done under St. Peter's leadership who had the vision (Acts 10) about it. St. Paul objected to Peter's personal behavior, but as we know from Scripture, it was Peter who initiated the reform. This was a doctrine that came from Peter and possibly John and James (Gal 1:9f, 2:1), so Paul could not be making a doctrinal point when he made his remark to Peter in Galatians 2:11f.
Peter was not called to the Jews in any exclusive sense -- it was Peter who opened the Chruch to the Gentiles (Acts 10) and converted the first Gentile (Acts 11).
The only way Peter could have founded the church at Rome was if he had appointed/commissioned the first leader of the church and sent him there. Paul wrote to the Romans and makes no mention of Peter's being there which is odd since he names so many others.
By the time Peter finally got to Rome, which I believe he did, and wrote a letter from there with the code word "Babylon" (I don't think he was literally at the ancient Babylon), someone else had already been leading the church; it could have been informally organized by early lay people, like I believe many others probably were in the earliest times, the leaders may have been "ordained" by the laying on of hands by one of the apostles.
That is not to say he couldn't have been the first pope, but I'm not fully convinced he was. It doesn't take many years for historians to get wrong information recorded that was handed down by word of mouth, and sadly, I think some writings were later altered to give more substance to claims.
I've read all the claims; none are totaly convincing one way or another.
Peter was converting Jews and learning to pass this along to Gentiles even tho he was stumbling while Paul was in Arabia learning first hand from God about the mystery of the adoption of the Gentiles, grace thru faith without works, eternal security, etc..