I’m not sure. It would be difficult to know unless one studied all papal statements and applied the infallibility criterion from the Vatican I Council to each.
Which ones are they?
I know of at least three off of the top of my head. The Assumption of Mary, the Immaculate Conception and Unam Sanctam.
Also as I understand it not everything in an ex-cathedral statement is infallible.
This isn’t exactly correct. The ex cathedra statement is infallible, but not everything contained in the Papal Bull/Apostolic Constitution that promulgates the dogma is.
This seems to be problematic.
Why do you think that? It’s no more problematic than identifying dogma contained in the decrees of an Ecumenical Council. Much contained in those documents treat disciplinary matters or explain the reasoning behind the dogmatic decrees, but they aren’t themselves infallible statements.
Should I take the general theme or the main point of all encyclicals?
In the modern papacy it is very rare that a Pope would use an encyclical as a vehicle to exercise the authority of the extraordinary Papal Magisterium. That does not mean though that a Catholic is free to disregard those teachings.
Can I pock and choose what I like and don’t like if it is fallible?
Generally the answer is “no.” The non-infallible teachings of the Pope must be given ordinary assent by Catholics.
How do councils fit into this?
Ecumenical Councils are called for the purpose of defining doctrine, usually in response to heresies that threaten the Catholic faithful.
I know that not everything in the council is ratified by the Pope.
Interesting. So far as I know every Ecumenical Council has been accepted or later ratified by the Pope. Local councils are a different matter.
You think that the church would make this easier for outsiders. Maybe the church has declared this and I just dont know.
I find it to be a non-issue with most neophytes who are approaching the Catholic faith. There are sources readily available to learn and understand what the Catholic Church teaches - most notably the Catechism. The ultimate source of authority for those teachings is generally of little concern - that is - whether the dogma was promulgated by an Ecumenical Council or by an ex cathedra statement of the Pope. The reasons behind the teachings are certainly relevant, but not the distinction between ex cathedra and non-ex cathedra pronouncements.