In his homily on this Epistle, St. John Chrysostomos expounds on the nature of St. Paul's care for the Churches. He says that this was the heaviest of the burdens with which St. Paul wrestled in his Apostolic ministry: "...His soul too was distracted, and his thoughts divided. For even if nothing from without had assailed him; yet the war within was enough, those waves on waves, that sleet of cares, that war of thoughts." St. John adds that, though it is difficult enough for one to look after a single house, St. Paul had "the care not of a single house, but of cities and peoples and nations and of the whole world" (Homily 12, in Nicene and Post-Nicene Fathers, First Series, Vol. XII [Grand Rapids, MI: Eerdmans, 1978], p. 395). Several Roman Catholic exegetes, in keeping with their misunderstanding of Christs words about the ministry of St. Peter, have misunderstood this all-embracing pastoral care with which St. Paul, as the Apostle to the Nations, was naturally entrusted as an institutional prerogative. In so doing, however, they once more compromise their own arguments. For, if St. Paul was given such care of all the Churches, then primacy in the Church would logically belong, again, not to St. Peter, but to St. Paul and, by implication, to his successors. Clearly, however, St. Paul was not speaking, in the passage under consideration, of an institutional prerogative, as St. John Chrysostomos points out, but of a burden imposed on him by the nature of his ministry.
With regard to the other verse which you cite, St. Theophylact of Ochrid points out that the words, "I will give unto thee,""...were spoken to Peter alone, yet they were given to all the apostles," since Christ also said, Whose soever sins ye remit, they are remitted." (The Explanation by Blessed Theophylact of the Holy Gospel According to St. Matthew [House Springs, MO: Chrysostom Press, 1994], p. 141.) The second verse to which St. Theophylact refers is St. John 20:23. As the translator rightly observes, the verb "remit" is in the second person plural, and thus refers not to St. Peter alone, but to all of the Apostles. As for the "controversial verse" (St. Matthew 16:18), St. Theophylact, following St. John Chrysostomos and the overwhelming consensus of both Greek and Latin Fathers, interprets the words "this rock" to denote St. Peters confession of faith in the Divinity of Christ, and not the Apostles person. Any other interpretation would, of course, violate the Christocentric nature of the Church and the rather clear Scriptural affirmation that "Christ is the head of the Church" (Ephesians 5:23) and the "head of the Body" (Colossians 1:18)."