Not according to history and even your own church. Not until at least the 4th century was there a single pope.
"The word pope derives from Greek πάππας meaning "Father". In the early centuries of Christianity, this title was applied, especially in the east, to all bishops and other senior clergy, and later became reserved in the west to the Bishop of Rome, a reservation made official only in the 11th century." [Schatz, Klaus (1996). Papal Primacy. Liturgical Press. pp. 28–29. ISBN 9780814655221.]
"The fourth canon of the First Council of Nicaea of 325 attributed to the bishop of the capital (metropolis) of each Roman province (the "metropolitan bishop") a position of authority among the bishops of the province, without reference to the founding figure of that bishop's see." [Canons of the First Council of Nicaea]
Domasus 366-384 - First to call himself Apostolic See
Leo the Great - 440-461 - first Pontifex Maximus
Prior to that the Pontifex Maximus was the secular ruler over the pagan religion who often presented himself as a god. An interesting read is how the early church fathers referred to that title.
The Catholic Church itself agrees there were many referred to as "pope".
The title pope, once used with far greater latitude, is at present employed solely to denote the Bishop of Rome" [http://www.newadvent.org/cathen/12260a.htm]
That unbroken line of popes is a fallacy. The rest of your posts is based on Old Testament and not applicable to the New Testament ekklesia of Christ.