Do the Catholics have a leader or authority?

Answer 1

It's just Catholic, not Roman Catholic. Roman is an epithet first commonly used in England after the protestant revolt to describe the Catholic Church. It is never used by the official Catholic Church.

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The leader AND the final authority of the Catholic Church is Our Blessed Lord, Jesus Christ, who is the head of the Church (see St. Paul 1 Cor 12:12-14, and Acts 9:1-5). He sent the Holy Spirit to guide it always (see John 14:26 & Luke 24:49). He appointed St. Peter (and his successors) as His Vicar on earth to rule over His Church (see Matthew 16:17-19 and Isaiah 22:15-25 on which it is based). Thus the visible leader and authority who represents Christ and is lead by the Holy Spirit is St. Peter's successor, the Pope in Rome. The "authority" for all Church teachings must be found in Sacred Tradition and Scripture, Sacred Tradition was closed with the death of the last apostle, St. John. The Sacred Scriptures were issued by the Church in the final form we have today in the late fourth century by Pope Damasus and the Council of Rome.

Answer 2

The pope is the temporal leader of the Catholic Church and holds the Church's highest position of authority under God. This authority means that the pope can make decisions independent of the college of bishops, that he can invoke the charisma of infallibility should he deliberately choose to if he must speak definitively upon a doctrine concerning the universal Church in Faith and Morals, he has jurisdiction to perform the sacraments and exercise his office anywhere in the world, he can promote or transfer whom he will, he can impose or lift religious sanctions on any of the faithful, and he can choose how to make available the graces of the Church through indulgences, pilgrimages, prayers, etc. The pope does not have authority to introduce new doctrines or beliefs or change Tradition.