To answer the first question, “What must be believed”
The answer is everything the Church teaches.
How do we know what the Church teaches?
Whenever the Bishops and the Pope teach together, as in a council, or in a Catechism, or whenever the Pope teaches by himself as head of the whole Church and his teaching is directed to the whole Church.
These teachings are also infallible.
And the Pope is also infallible in these teachings, when he teaches by himself.
There are two types
If they are clear explanation of some doctrine of faith or morals to be definitely held, and he is teaching as the head of the Church, this is called an Ex Cathedra teaching.
If he is not clearly giving a thorough explanation of some doctrine of the faith, but he is just repeating some matter, over and over as an extension to the faith, and we see he is clearly intending to teach , then divine assistance is also given and this is ordinary teaching and it is infallible.
This is taught in the Catechism below, where the Catechism describes the two types of teachings, the first in regards to clear explanations concerning the deposit of faith, and the second are the ordinary teachings which may include extensions to the deposit of faith.
890
To fulfill this service, Christ endowed the Church’s shepherds with the charism of infallibility in matters of faith and morals. The exercise of this charism
takes several forms:
- “The Roman Pontiff, head of the college of bishops, enjoys this infallibility in virtue of his office, when, as supreme pastor and teacher of all the faithful - who confirms his brethren in the faith he proclaims by a definitive act a doctrine pertaining to faith or morals… The infallibility promised to the Church is also present in the body of bishops when, together with Peter’s successor, they exercise the supreme Magisterium,” above all in an Ecumenical Council.[418] When the Church through its supreme Magisterium proposes a doctrine “for belief as being divinely revealed,”[419] and as the teaching of Christ, the definitions “must be adhered to with the obedience of faith.”[420] This infallibility extends as far as the deposit of divine Revelation itself.[421] † ©
- Divine assistance is also given to the successors of the apostles, teaching in communion with the successor of Peter, and, in a particular way, to the bishop of Rome, pastor of the whole Church, when, without arriving at an infallible definition and without pronouncing in a “definitive manner,” they propose in the exercise of the ordinary Magisterium a teaching that leads to better understanding of Revelation in matters of faith and morals. To this ordinary teaching the faithful “are to adhere to it with religious assent”[422] which, though distinct from the assent of faith, is nonetheless an extension of it.
Notice in 892 he is not arriving at an infallible definition and it is not pronounced in a “definitive manner”, thus it is not necessarily directly part of divine revelation, but is is an extension of divine revelation. Since divine assistance is also given in this case the Pope is still teaching infallibly.
Thus infallibility is given in both extraordinary teachings and ordinary teachings.