Yes, this is true, however like someone else said, they do not have the authority to call an Ecumenical Council without the authority of the Pope. Without the Papal Authority no Ecumenical Council could be Infallible.
Untrue.
All that is required a an intent to gather, and the gathering of the bishops, it is the combined authority of the bishops, and the subsequent acceptance by the church at large, which make a council infallible. Call it what you like.
Now I am beginning to think eastern and western Christians are not in full agreement as to what infallibility of a Council implies. It is not a type of perfection. One Council can reverse the decision of a prior council. One bishop cannot do that, but a subsequent Council can.
The notion is the Paraclete is with us, and the actions of a council of bishops are acceptable to the Holy Spirit.
No Good Housekeeping Seal required. If the church at large accepts it thatās a good thing.
The title of ecumenical originally did mean the empire. The theory was there should be one earthly kingdom under God. I suppose the Romans had harbored a notion that theirs was it. They had suddenly developed great ambitions for a single worldwide Christian State (other states have since thought that way too at times). When the First Ecumenical Council was called virtually everyone who was a Christian was already within the bounds of the Roman State (which paid the costs for the gathering, BTW). (Armenia may have been independent at that point, and there were some colonies of Christians elsewhere, like India).
Thus, this was much more than the regional councils of bishops of the previous two hundred years, it was essentially all the regional councils meeting simultaneously, in effect. Thatās what made it so important and why it was so readily accepted across the church. There is no magic to it.
The bishop of Rome would not have chaired the Council, it was hosted in Nicea. He would have received just one vote, like any other bishop in attendance. Naturally they would have been interested in his opinions, being from such an important See. But the bishop did not even attend and whether or not he would have liked it, the Council did not need him. The same is true today.
Anything the Latin church teaches about that differently today is evolved thinking that did not hold true at the time.