Awesome.

Here is a short introduction to the types of Catholic teaching. First, the teaching office of the Church is called the "magisterium", from the Latin magister -- "teacher".

Basically, there are two sorts of teaching, infallible and not infallible. The qualifications for an infallible teaching are set out in section 25 of Vatican II's Dogmatic Constitution on the Church, Lumen Gentium -- "Light of the Nations" -- online here among other places. LG 25 says that there are three modes of infallible teaching: (1) an ex cathedra pronouncement from the pope, (2) a solemn declaration of a council, and (3) the pope and the college of bishops exercising "the universal and ordinary magisterium".

The first two are fairly straightforward: Ex cathedra -- "from the chair", i.e., the papal throne -- pronouncements have been made exactly twice: Pius IX's proclamation of the Immaculate Conception in 1864 and Pius XII's proclamation of the Assumption of Mary in 1950. A decree from a properly constituted ecumenical council is also easy -- LG is one, for example.

The third, the universal and ordinary magisterium, is described in LG 25 as

Although the individual bishops do not enjoy the prerogative of infallibility, they nevertheless proclaim Christ's doctrine infallibly whenever, even though dispersed through the world, but still maintaining the bond of communion among themselves and with the successor of Peter, and authentically teaching matters of faith and morals, they are in agreement on one position as definitively to be held.

For reasons of ecclesiastical politics, meetings of the bishops have been few and completely dominated by the Pope and the Vatican curia. There hasn't been one for over 25 years, and the last few were exercises in futility -- essentially, the Vatican presented its position and forbade meaningful debate on it.

As for non-infallible papal teaching -- the "ordinary papal magisterium" -- and teachings by individual bishops, LG 25 says

Bishops, teaching in communion with the Roman Pontiff, are to be respected by all as witnesses to divine and Catholic truth. In matters of faith and morals, the bishops speak in the name of Christ and the faithful are to accept their teaching and adhere to it with a religious assent. This religious submission of mind and will must be shown in a special way to the authentic magisterium of the Roman Pontiff, even when he is not speaking ex cathedra; that is, it must be shown in such a way that his supreme magisterium is acknowledged with reverence, the judgments made by him are sincerely adhered to, according to his manifest mind and will. His mind and will in the matter may be known either from the character of the documents, from his frequent repetition of the same doctrine, or from his manner of speaking.

"Religious assent" means that the faithful are to read the teaching carefully, pray for guidance, give the teaching the benefit of any possible doubt. However, if one cannot accept the teaching, one should reject it. Thomas Aquinas says that a conscience, even an erring conscience, must be followed, even if it goes against Church teaching. (See his Summa Theologica, I, question 79, article 13.)

When he was Prefect of the Congregation for the Doctrine of the Faith before becoming Pope Benedict XVI, the then Cardinal Ratzinger tried to push a new category of teaching, the "definitive teaching". These teachings are intended to be de facto infallible, even if they do not meet the de jure definition. The term for this sort of thing is "creeping infallibility", and has no actual support either historically or theologically.

This just touches the surface of a fairly complex subject, and if you have questions, I shall attempt to answer them.

It is incorrect to say that "religious assent" gives the catholic the right to reject church teachings they don't like. I will post more about it eventually, but this article covers the topic thoroughly: http://www.twotlj.org/G-2-1-I.html

Means that any Catholic can reject non-infallible teachings. It means that one is to study the teaching, consider it carefully, pray for understanding. But it does not mean, as

Tell me, georges, do you believe that taking interest on a loan is morally acceptable? Then you are a Cafeteria Catholic.

Do you believe that socialized medicine is wrong? Then you are a Cafeteria Catholic, since both Pope John Paul II and the United States Conference of Catholic Bishops say that healthcare is a right of all people.

Do you accept capital punishment? Then you are a Cafeteria Catholic, since and yes, the current moral teaching is that capital punishment is not immoral per se, but there are essentially no circumstances under which it is moral. Your bleating that the state is competent to make such a decision is flawed. Harvey Cox wrote an essay, "On Not Leaving It To The Snake". In it, he interprets the sin of Adam as a sin of sloth. Sloth is generally seen as laziness, but the word for it in Latin is acedia, which means "uncaring". Eve let the snake make the decision to eat the fruit for her, and Adam let Eve make the same decision for him. They both left the moral decision up to someone else -- ie, they did not care to make their own decision.

I wish to remind you of Adolf Eichmann's defense of "I was just following orders." This defense was rejected because Eichmann was trying to claim that he allowed his superiors to make moral decisions for him. He knew what he was doing, he was, after all, the secretary at the Wannsee Conference.

No, we must make our own moral decisions. Thomas Aquinas taught that we must follow our consciences, even if our moral advisors tell us that we are wrong. Above all, we must not leave moral decisions to others.

No, georges you are just as much at the cafeteria as anyone else.

No I'm not picking and choosing. The church says the state has that right, not me. I yield to the church.

What do you think about the state having the right to permit the unborn to be eliminated?

Do you agree with the state or the church?

No I'm not picking and choosing. The church says the state has that right, not me. I yield to the church.

No, the Church says that capital punishment is not immoral per se, but there are essentially no cases in which it is licit.
It does NOT say "leave it up to the state", and you are wrong when you say that it does. Obviously, you reject what the Church teaches, and are unwilling to admit it. Incidentally, I gave a specific source for my belief on what the Church teaching is. What is your source? Be specific.

What do you think about the state having the right to permit the unborn to be eliminated?

Well YOU certainly have no problem with the state saying it. After all, you are perfectly willing leave the question "who is to be killed?" up to the state.

to discussion?

If the new Pope said they were open to discussion, they would be open to discussion.

Two points: Don't hold your breath for this to happen; and both topics are actually being discussed. I have posted on both in DU.