There has been a lot posted here since my last visit, so I am going to respond in one post to only a few remarks; otherwise I will be here all night.
I have cited my sources. If you think the English translations of those sources are inaccurate, you are welcome to prove it.
With regard to the pope being he head. I'll just give a couple quotes in order to avoid confusion and complexity. Emphases mine.
St. Theodore the Studite wrote to Pope Leo III:
"To the most holy and chiefest father of fathers, to my lord Leo, apostolic pope— Theodore, lowliest of priests and abbot of Studion. Since it is to the great Peter that Christ our God gave the keys of the kingdom of heaven along with the dignity of chief shepherd, it is to Peter, that is, his successor, that it is necessary to refer every innovation which is made in the Catholic Church by those who turn aside from the truth. That is what we humble and lowly monks have learned from the ancient fathers. Therefore, because a new teaching has arisen in the midst of the Church here, we believed that we ought to submit it to the messenger of your supreme beatitude, first through one of our fathers, the most holy archimandrite Epiphanius, and then by this simple letter. O divine head of all heads, a synod of prevaricators has been held, as the prophet Jeremias says— a council of adulterers. These men have not been content to conspire in favor of the priest who blessed the adulterous marriage and to receive him into communion, but, to merit the name of perfect heretic, have excommunicated in a second synod those who do not cleave to their error, or rather the Catholic Church itself.".. [PG 99: 1017 sq.].
Pope Boniface I (+422) wrote to the bishops of Thessaly:
"The institution of the universal Church at its birth took its beginning from the office of Blessed Peter, in whose person its government and summit consists. For from his fountain the stream of ecclesiastical discipline flowed forth into all the Churches, as the culture of religion progressively advanced. The precepts of the Council of Nicea bear witness to nothing else: so that it did not dare to appoint anything over him, seeing that nothing could possibly be conferred above his office: moreover, it knew that everything had been granted to him by the word of the Lord. Certain, therefore, is it that this [Roman] Church is to the Churches spread throughout the world, as it were, the head of its own members, from which whoever cuts himself off is expelled from the Christian religion, inasmuch as he has ceased to be within the one structure. I hear that certain bishops, despising the apostolic right, have attempted anew to undermine the precepts of Christ Himself, since they are striving to separate themselves from the Apostolic See’s communion, or if I may speak more accurately, her authority, asking for help from those to whom ecclesiastical rules have not sanctioned any greater authority... Receive, therefore, our admonition and rebuke: one of which we offer to the pontiffs [siding with us], the other to the dissidents. For you know that either one is possible to Blessed Peter: that is, to correct the meek with meekness, or to rebuke the haughty with the rod. Show therefore due honor to the head, for we do not want the members to be fighting with each other, with their quarrels reaching all the way to us, while you hold in contempt our brother and fellow bishop Rufus, to whom our authority granted nothing new, following the precedent by which the care of the churches was enjoined on him. We want this to be observed holy and inviolate, as the decree of this disposition has been kept by the fathers, for it is unfitting for the brethren to be irked at the dignity of another. If anybody was punished excessively, without question there should have been an appeal to us, in whom, as you know, care of all remains, and a delegation sent, because for this purpose the Apostolic See holds the principality, so that it may receive the lawful complaints of all... Let this novel presumption cease. Let nobody strive to undermine what has been done by the fathers, and observed for so long. Whoever accounts himself a bishop, let him obey our ordinance. Let nobody presume to ordain bishops anywhere in Illyricum without the knowledge of our fellow bishop Rufus... [PL 20: 777-79].
In 485, a Roman synod of 43 bishops met to consider the case of Antioch, where the orthodox patriarch Calendion had been ejected and replaced by Peter the Fuller. On October 5, the synod wrote to the orthodox clergy and archimandrites of Constantinople:
“From the beginning, the faith of your holiness has been proven to the Apostolic See, which rules over us all.” The synod offered this explanation of Roman custom and procedure: Now, therefore... gathered before [the tomb of] the most blessed apostle Peter, again we have hastened to inform Your Love of the custom that has ever obtained among us. As often as the bishops of the Lord gather together within Italy to deal with ecclesiastical matters, especially matters of faith, the custom is retained that the successor of the bishops of the Apostolic See establish provisions for all matters in accordance with the solicitude for all the churches which is proper to him who is the head of all, as the Lord says to Blessed Peter: ‘Thou art Peter...’ Following this saying, the 318 Fathers who met at Nicea referred the confirmation of matters to the holy Roman Church... [CSEL 35: 158-9].
The Decree of Pope Damasus (362)
"Likewise it is decreed: ...we have considered that it ought to be announced that although all Catholic churches throughout the world comprise but one bridal chamber of Christ, nevertheless the holy Roman Church has been set before the other churches not by any synodical decrees but by the evangelical voice of our Lord and Savior, saying: “Thou art Peter, and upon this rock I will build my Church, and the gates of hell will not prevail against it; and I will give to you the keys of the kingdom of heaven, and whatsoever you shall bind on earth shall be bound in heaven, and whatsoever you shall loose on earth shall be loosed in heaven.” The first see, therefore, is that of Peter the apostle, that of the Roman Church, which has neither stain nor blemish nor anything of the kind. The second see was consecrated at Alexandria, in the name of Blessed Peter, by his disciple the evangelist Mark, and he, having been sent by St. Peter into Egypt, preached the word of truth and consummated a glorious martyrdom. The third see [of the most blessed apostle Peter] is at Antioch, which is considered honorable because he lived there before he came to Rome, and there the name of the new nation of Christians first arose." [PL 13: 374-6].
Notice, according to Pope Damasus the primacy is a divine primacy coming from Christ, not from counsels.