Peter was the first STEWARD of the Church. Given his special authority as Apostle, one "can" argue that that elevates him above mere "pope-hood". But he certainly DID ordain the second Steward. Whether that individual was the first Pope or the second is open to interpretation.
I don't think so. Whether Peter was something MORE than Pope or not, he was still Pope first. The official list of Popes is good enough for me. Linus I may have been the first to be merely Pope, but he was the second Pope, after Peter.