Actually, no. After Matthew 16:18, Jesus tells Peter "what you open, no one may shut, what you shut, no one may open. That's where Infallibility comes from. I don't know what "Jurisdiction" is, can you explain?
If you believe the Lady is Immaculate, where did that come from, and when?
When ever I have come across this quote it has been from Revelation , To the people of Sardis if I remember aright, but I have failed to come across any mention of S. Peter, I might have read it wrongly or my memory is faulty? There's certainly no mention of the Pope in his pseudonym or as the bishop of Rome?
Christ is infallible and Ecumenical Councils, when they are accepted freely by the Church .Certainly not the Pope.
Jurisdiction?
According to Wikipedia Article ;",By Divine Law, the Pope has Ordinary Jurisdiction,over the entire church."It is one of the Complaints made about Trent, was that the Bishops of Northern Europe abdicated their Christ given responsibilities on to the shoulders of the Bishop of Rome, this by refusing to vote on the Council till it had been passed
As I understand there are two ways the Bishop of Rome claims superior jurisdiction, one over territory in the 'Temporal realm of Earth'. I.E. It was the Bishop of Rome that ,'gave,' a free Ireland unto the English King, Henry II, Later he involved himself in to English Politics, as I mentioned earlier.
Secondly the Pope involved himself in the Sees of other Bishops without being asked or without permission.and broke the Canons of the Ecumenical Council. ( Niceae.) Another one called a Council at Trent and named it an Ecumenical Council, which is not his perogative. Further the bishops of the Church on the Continent abdicated their Christ given spiritual and ecclesiastical responsibilities on to the shoulders of the Roman Bishop. Regarding the Lady Mary?
1st, Ephesus, defined Mary as the 'Theotokos,' i.e. The Mother of God.
2nd, Council of Constantinople, 9381.) Twice referred to Mary as the,'Ever Virgin.'
2nd, Council of Ephesus, Defined Mary as being Spotless and Immaculate.
Again we have nothing to say about an Immaculate Conception.
Infact one of our scholars, Bishop Field referred to the latter council as being of ,manners, considering it crude and unpleasant to discuss the Lady Mary in such terms. (Field. Google Books. )