Where does Paul write about the Roman Catholic church in his letters?
There was no separate Roman Rite when the NT was written. Neither was there when it was canonized in the 4th century.
Where does he even come close to mentioning praying to Mary and the saints?
Scripture has many references that we should pray one for another. Jesus taught us that when we are in Him, we will never die. We believe that those in Christ have eternal life, and that they cannot be separated even by death. Note how the writer of Hebrews speaks about the part of the Holy Church that is already in heaven:
Heb 12:22-24
22 But you have come to Mount Zion and to the city of the living God, the heavenly Jerusalem, and to innumerable angels in festal gathering, 23 and to the assembly of the first-born who are enrolled in heaven, and to a judge who is God of all, and to the spirits of just men made perfect, 24 and to Jesus, the mediator of a new covenant, and to the sprinkled blood that speaks more graciously than the blood of Abel.
This is the sinless part of the Church, ja4. This part of the Church, unlike those of us who are not yet made perfect in faith, they can no longer sin, as they have been purified. No sin exists in heaven. The spirits of just men made perfect, are in the best position to pray for us, even more so than we are for one another, because they have already laid aside every weight and sin which so easily besets us.
Where does he write that church leadership requirement should be celibate men for example?
I don’t see that it does, but I also don’t see that this is relevant, either, since this is not the teaching of the Catholic Church either.
Where does Paul write about Apostolic succession in his letters?
“…what you have heard from me before many witnesses entrust to faithful men who will be able to teach others also.” 2 Tim 2:2
This represents four generations of Apostolic succession, ja4. THe Apostle has given the Sacred Traditions to TImothy, who is to entrust that Divine Deposit of Fatih to faithful men, who are able to teach others also. This is the office and ministry of the bishop.
What makes you think that Peter was ruling from Rome the entire church? What evidence is there for this?
I think nothing of the sort. In fact, I think you idea of “supremacy” and “ruling” is a contamination from Paganism. This is a secular attitude about leadersthip, and has no place in God’s kingdom. I think the NT is very clear on this point. I am surprised to hear that you would espouse such an anti-scriptural attitude! But, none of us are perfect. In fact, we all fall short in many ways. Many people, including some of the Popes, had their understanding of leadership perverted by the world, the flesh, and the devil. I just don’t see that Peter was one of them.