Not every ecumenical council does all three things.
(The term 'ecumenical' comes from the Greek word 'oikoumene', 'the whole inhabited world'.)
The first known regional council was the Council of Jerusalem in 52 A.D. (Acts of the Apostles, chapter 15). Its decrees were both doctrinal (circumcision is not necessary for salvation) and disciplinary (Christians should not eat meat that had been sacrificed to an idol).
Most of the bishops of the eastern Empire came, and many from the west. Pope Sylvester I was sick, but he sent delegates to represent him. There were about 318 bishops present.
The precise phrasing of the Creed, 'begotten, not made, one in being with the Father' - or, 'of the same substance as the Father' - was intended to exclude Arius' false teaching that Christ is not God.
Several decrees on the Eucharist, especially re: the Real Presence of Christ and transubstantiation
In these sessions the bishops issued further doctrinal decrees about the nature of the Eucharist, and the Church's power to make arrangements about the celebration of the Mass (e.g., communion under both kinds, or only under the form of bread; whether & at what age small children can receive communion, etc.). They discussed whether to allow the Mass to be celebrated in local dialects and decided against it. There were also both doctrinal and disciplinary decrees about the sacraments of Orders and Matrimony.
Protestants were invited to these sessions, but most refused to come and no common ground for discussion could be found with the few who came.
A profession of faith and catechism were drawn up based on the decrees of the council - not to replace the Nicene Creed (which is still said in the Mass today), but for use in receiving converts from Protestant sects.
These books the church holds to be sacred and canonical not because she subsequently approved them by her authority after they had been composed by unaided human skill, nor simply because they contain revelation without error, but because, being written under the inspiration of the holy Spirit, they have God as their author, and were as such committed to the church.
...when the Roman pontiff speaks ex cathedra, that is, when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his supreme apostolic authority, he defines a doctrine concerning faith or morals to be held by the whole church, he possesses, by the divine assistance promised to him in blessed Peter, that infallibility which the divine Redeemer willed his church to enjoy in defining doctrine concerning faith or morals.
Sources
Prepared by Jim Henry
9 September 2001