Is Peter the first pope the same Peter that denied Jesus?

No. The disciple Peter, who is reported to have denied Jesus three times, lived in the first half of the first century, but the two epistles that bear his name are clearly works written in the second century. In fact, 2 Peter incorporates almost all of the Epistle of Jude*, itself a second-century work. Not only would the apostle Peter not have had to copy the work of a lesser disciple, he could not have done so in the second century.

* Jude was written as if by either the apostle Jude or by Jude the brother of Jesus, but speaks (Jude 17-18) somewhat carelessly of the disciples as people who had lived in the distant past.