“An Ecumenical Council, according to the Catholic faith, is always the supreme teaching authority of the Church.” This is at best sloppy, and at worst an academic lie. First it omits the fact that the acts of a Council must be confirmed by the Pope to have authority; this is perhaps of only technical interest, since the Second Vatican Council (V2) was confirmed by the Pope. More important, it blurs the critical distinction between act and potency: a Council has the power (potential) to exercise supreme teaching authority (in union with the Pope), but whether it decides to use that power is the question. V2 explicitly declined to use that power, and Pope Paul VI explicitly said that it had not used it. (Note that I think I am using the term “supreme teaching authority” in the same sense in which it appears to be used in the context of the above quote, meaning that anything said by such authority is at the level of irreformable dogma and Divine Revelation.)
You are incorrect. By definition an ecumenical council has been confirmed by the Pope, otherwise it is not in communion with the Pope and not ecumenical.
Definition of terms. By definition, an Ecumenical Council is always the supreme authority, ect.