About Biblical inerarncy and Papal infallibility

Biblical Inerrancy
Ecumenical Church has never confessed a dogma about the Bible "we believe that Bible is...".

However, Nicene Creed refers at the crucial point of the credo to the authority of the Scriptures
Et resurréxit tértia die, secúndum Scriptúras

In the modern times 300 evangelical leaders in the USA decided to write such a dogmatic confession about the Bible.

THE CHICAGO STATEMENT ON BIBLICAL INERRANCY

4. Being wholly and verbally God-given, Scripture is without error or fault in all its teaching, no less in what it states about God's acts in creation, about the events of world history, and about its own literary origins under God, than in its witness to God's saving grace in individual lives.
Church documents

Papal infallibility

Papal infallibility is a dogma of the Catholic Church which states that, by action of the Holy Spirit, the pope is preserved from even the possibility of error when in his official capacity he solemnly declares or promulgates to the universal Church a dogmatic teaching on faith or morals. It is also taught that the Holy Spirit works in the body of the Church, as sensus fidelium, to ensure that dogmatic teachings proclaimed to be infallible will be received by all Catholics. This dogma, however, does not state either that the pope cannot sin in his own personal life or that he is necessarily free of error, even when speaking in his official capacity, outside the specific contexts in which the dogma applies.

This doctrine was defined dogmatically in the First Vatican Council of 1870. According to Catholic theology, there are several concepts important to the understanding of infallible, divine revelation: Sacred Scripture, Sacred Tradition, and the Sacred Magisterium. The infallible teachings of the pope are part of the Sacred Magisterium, which also consists of ecumenical councils and the "ordinary and universal magisterium". In Catholic theology, papal infallibility is one of the channels of the infallibility of the Church. The infallible teachings of the pope must be based on, or at least not contradict, Sacred Tradition or Sacred Scripture. Papal infallibility does not signify that the pope is impeccable, i.e.., that he is specially exempt from liability to sin.

The doctrine of infallibility relies on one of the cornerstones of Catholic dogma—that of petrine supremacy of the pope, and his authority to be the ruling agent in deciding what will be accepted as formal beliefs in the Church. The clearest example (though not the only one) of the use of this power, referred to as speaking ex cathedra[4] expressed since the solemn declaration of papal infallibility by Vatican I on July 18, 1870, took place in 1950 when Pope Pius XII defined the Assumption of Mary as being an article of faith for Roman Catholics. This authority is considered by Catholics to be apostolic and of divine origin. Prior to the solemn definition of 1870, Pope Boniface VIII in the Bull Unam Sanctam of 1302, Pope Eugene IV in the Bull Cantate Domino of 1441, and Pope Pius IX in the Papal constitution Ineffabilis Deus of 1854 have all spoken "ex cathedra."
wikipedia