Was Peter the first pope? Did the bishop of Rome rule the whole church?

Ignatius of Antioch d. c. 110 ADLetter to the Romans Preface

... the church which presides in the place of the region of the Romans, worthy of God, worthy of honor, worthy of blessing, worthy of praise, worthy of success, worthy of holiness, and presiding in love ...

Ignatius gives Rome a greeting he gives no other church, but names no bishop of Rome. "Presiding in love" is read as a primacy by some and as a primacy of charity by others.

Cyprian of Carthage c. 200–258 ADOn the Unity of the Church 4

He builds the Church on one man. And although after his resurrection he gives equal power to all the apostles ... yet to show unity he arranged by his authority that the origin of that unity should begin from one. The other apostles were certainly what Peter was, endowed with an equal share of honor and power, but the beginning starts from unity, so that the Church of Christ may be shown to be one.

This is the "received text". A second version of the chapter, also from Cyprian's hand, adds "primacy is given to Peter" and speaks of "the chair of Peter".

Firmilian of Caesarea d. c. 269 ADLetter 75, to Cyprian 75.17

I am rightly angry at this open and plain folly of Stephen: he who boasts so of the place of his episcopate and claims to hold the succession of Peter, on whom the foundations of the Church were laid, brings in many other rocks and sets up new buildings of many churches.

An Eastern bishop, in Cyprian's Latin, mocks Rome's claim during the rebaptism dispute. It shows the claim was being made by 256.

Optatus of Milevis fl. c. 365–c. 385 ADAgainst Parmenian the Donatist 2.2

You cannot deny that you know that in the city of Rome the episcopal chair was first given to Peter, in which sat Peter, the head of all the apostles, which is why he was called Cephas; that in this one chair unity might be kept by all, so that the other apostles would not each defend their own, and that whoever set up another chair against the single chair would already be a schismatic and a sinner.

Optatus goes on to list the bishops of Rome down to Siricius.

Council of Constantinople (as Socrates reports)Socrates, Church History 5.8

Then they also issued a decree that the bishop of Constantinople should have the privileges of honor after the bishop of Rome, because it is New Rome.

Canon 3 ties rank to the imperial capital. Rome did not accept it for centuries, nor Chalcedon's canon 28, which went further.

Council of CarthageCanons of the African Church Canon 28 (Codex 34)

If they think they must appeal, let them not appeal to courts across the sea, but to the primates of their own provinces or to a general council ... Whoever thinks he must appeal across the sea, let no one in Africa receive him into communion.

"Across the sea" means Rome. The African bishops, Augustine among them, resisted Roman appeals in the case of Apiarius.

Westminster AssemblyWestminster Confession of Faith 25.6

There is no other head of the church but the Lord Jesus Christ. Nor can the pope of Rome, in any sense, be head thereof.

The 1646 text goes on to call the pope "that Antichrist". American Presbyterians removed the phrase in 1788.

First Vatican CouncilPastor Aeternus Chapter 2

Therefore whoever succeeds to the chair of Peter obtains by the institution of Christ himself, the primacy of Peter over the whole church.

The Catholic definition. Chapter 4 adds that the pope is infallible when he defines ex cathedra.