The RC will say yes, as infallibility promised to the office, and not contingent upon the holiness of the person, and is assured whenever the world wide bishops in an ecumenical assembly speak together in union with the pope on faith and morals, or the pope himself, even autocratically regardless of what the bishops think or do .
In support they will invoke Caiaphas, who being high priest that year, he prophesied that Jesus should die for that nation, by advising that it was expedient that one man should die for the people. (Jn. 11:49-52)
The problem with that is that there was no assurance when he would prophecy, which Pharaoh (Ex. 10:28) and the people of the Jews also did (Mat_27:25). There was no assurance even when he would speak truth, but this text simply supports that he would at some time.
Moreover, while his counsel was a prophetic truth, that one man should die for the people, he was actually leading his people into wrath by the intent in which it was given.
Furthermore, in Scripture we see both writings and men of God were recognized and established as being so (essentially due to their heavenly qualities and attestation) , and Truth preserved, without an assuredly infallible magisterium, and too often in spite of the magisterium. Thus the church began in dissent from those who sat in the seat of Moses, being the stewards of Scripture, not upon the premise of assured magisterial infallibility.
Thus both Caiaphas and Scripture at large it fails to support the premise that the office of the pope alone or the magisterium of ecumenical counsels with him will perpetually be infallible when ever they universally speak on faith and morals.
In addition is the Scriptural and historical testimony against Peter and early successors being looked upon as exalted supreme infallible heads over all the church.
The question then is, what is the basis for RC assurance that Rome is the one true and infallible church? History, Scripture and Tradition can only authoritatively mean what Rome says they do.
And the reality for a RC is that Rome has presumed to infallibly declare she is and will be perpetually infallible whenever she speaks in accordance with her infallibly defined (scope and subject-based) formula, which renders her declaration that she is infallible, to be infallible, as well as all else she accordingly declares.
B.) Was Mary's (the Mother of Jesus) mother immaculately conceived as Mary was?
The question being, if Mary could be preserved sinless though having impure progenitors, so could Christ have been. And God brought forth His pure written word thru imperfect men.
Moreover, the fact is that the Holy Spirit characteristically records notable exceptions to the norm, from extreme ages, to height, to talking donkeys, to extra toes, to long-term virginity, etc. to sinlessness, thus Christ is at least thrice recorded as being so.
Based upon the silence hermeneutic Catholics invoke in support (it does not say she sinned) of the IC and other aspects of the hyper exaltation of the Mary of Catholicism beyond what is written, (cf. 1Cor. 4:6) then Paul never manifestly sinned after his conversion, while it could be taught that Mary will be one of the two witnesses in Revelation.
C.) When the Apostle Paul confronted Peter (when Peter was being hypocritical concerning his eating with Jews and Gentiles), did the Apostle Paul possess infallibility
That posses no problem in erroneous RC theology, as see the first question. Neither scenario fits the RC criteria, but neither does Paul's description of James, Cephas and John (in that order) "who seemed to be pillars", and his subsequent rebuke of Peter, support RC papal adulation and feet kissing,which Paul says nothing akin to.
Of course, then you have the 51 Biblical Proofs Of A Pauline Papacy (parody)
D.) During the time of the Western Great Schism of 1378, if papal infallibility was in existence at that time (and only later just codified), how could any person who was not one of the two Popes infallibly know (if they did not possess any measure of infallibility) which POpe was legitimate until this was later worked out? What about that period of time? Were people left "twisting in the wind?"
Indeed.
Referring to the schism of the 14th and 15th centuries, Cardinal Ratzinger observed
, "For nearly half a century, the Church was split into two or three obediences that excommunicated one another, so that every Catholic lived under excommunication by one pope or another, and, in the last analysis, no one could say with certainty which of the contenders had right on his side.
The Church no longer offered certainty of salvation; she had become questionable in her whole objective form--the true Church, the true pledge of salvation, had to be sought outside the institution. It is against this background of a profoundly shaken ecclesial consciousness that we are to understand that Luther, in the conflict between his search for salvation and the tradition of the Church, ultimately came to experience the Church, not as the guarantor, but as the adversary of salvation. (Joseph Cardinal Ratzinger, head of the Sacred Congregation of the Doctrine of the Faith for the Church of Rome, “Principles of Catholic Theology,” trans. by Sister Mary Frances McCarthy, S.N.D. (San Francisco: Ignatius, 1989, p.196; http://www.whitehorseinn.org/blog/2012/06/13/whos-in-charge-here-the-illusions-of-church-infallibility/)
The Western Schism was thus at an end, after nearly forty years of disastrous life; one pope (Gregory XII) had voluntarily abdicated; another (John XXIII) had been suspended and then deposed, but had submitted in canonical form; the third claimant (Benedict XIII) was cut off from the body of the Church, "a pope without a Church, a shepherd without a flock" (Hergenröther-Kirsch). It had come about that, whichever of the three claimants of the papacy was the legitimate successor of Peter, there reigned throughout the Church a universal uncertainty and an intolerable confusion, so that saints and scholars and upright souls were to be found in all three obediences. On the principle that a doubtful pope is no pope, the Apostolic See appeared really vacant, and under the circumstances could not possibly be otherwise filled than by the action of a general council. - http://www.newadvent.org/cathen/04288a.htm
Interesting. When I read this, the following thought popped into my mind: If Christ had to have impure progenitors in order to be sinless, then by reasoning, Mary is better than Christ because she could overcome having an impure lineage. Therefore, she must be "better" that Christ Jesus. Egads - blasphemy!
By RC reasoning (that Jesus had to have some help in coming from a sinless mother), either all of Mary's ancestors had to be sinless, or Mary is greater than Jesus.