Which church council sought to address internal problems and the challenges brought by Protestants?

Answer 1

The Council of Trent addressed internal church problems and the challenges brought by the Protestants.
The 19th Ecumenical Council of the Church was summoned for the purposes of 1) reforming the Church, and 2) combating Protestantism. The nineteenth ecumenical council opened at Trent on 13 December, 1545, and closed there on 4 December, 1563. Its main object was the definitive determination of the doctrines of the Church in answer to the heresies of the Protestants; a further object was the execution of a thorough reform of the inner life of the Church by removing the numerous abuses that had developed in it. The Council of Trent was called by Paul III who was pope from 1534 to 1549 and it first sat in December 1545.

from The Catholic Encyclopedia article on the Council of Trent

The Ecumenical Council of Trent has proved to be of the greatest importance for the development of the inner life of the Church. No council has ever had to accomplish its task under more serious difficulties, none has had so many questions of the greatest importance to decide. The assembly proved to the world that notwithstanding repeated apostasy in church life there still existed in it an abundance of religious force and of loyal championship of the unchanging principles of Christianity. Although unfortunately the council, through no fault of the fathers assembled, was not able to heal the religious differences of Western Europe, yet the infallible Divine truth was clearly proclaimed in opposition to the false doctrines of the day, and in this way a firm foundation was laid for the overthrow of heresy and the carrying out of genuine internal reform in the Church.

from A Catholic Dictionary, edited by Donald Attwater, Second edition, revised 1957

The Council of Trent

The 19th ecumenical council held at Trent in the Austrian Tyrol, 1545-63, summoned for the purpose of combating Protestantism and reforming the discipline of the Church; the longest and one of the most important of all general councils. It dealt in detail with the doctrinal innovations of the Reformers and with those gross abuses which gave them an opportunity to take root. It was one of the most important events of modern history and has had lasting effect. The principal dogmatic decisions were: the confirmation of the Nicene creed; the authenticity of the Latin Vulgate and the canonicity of all books contained therein and of them only; the definition of the doctrine of Original Sin; the precision of the doctrine of Justification, condemning justification by faith alone and imputation of grace; the condemnation of thirty errors about the sacraments; the definition of the Real Presence and of Transubstantiation as its mode: the precision of the doctrine of the sacraments of penance and Extreme Unction; the declaration that holy communion in both kinds was not necessary for lay-people and clerics not celebrating, Christ being received whole and entire under either species; the precision of doctrine concerning the sacrifice of the Mass and the sacraments of holy Orders and Matrimony; the affirmation of the doctrines of Purgatory, of the invocation of saints, and the veneration of them, their relics and images, and of Indulgences. Far-reaching decrees of reformation in discipline and morals were adopted involving many alterations in canon law, e.g. the decree Tametsi.