Short answers, pulled from the story.
J. R. R. Tolkien was a devout Roman Catholic from boyhood who described The Lord of the Rings as a fundamentally religious and Catholic work that became consciously so during revision.
Tom Shippey notes that the destruction of the Ring and the fall of Sauron take place on the 25th of March which is the traditional Anglo-Saxon date of the crucifixion of Christ and the annunciation.
Gandalf serves as a prophet who dies in Moria and returns reborn as Gandalf the White while Frodo acts as a priest carrying a burden of evil and Aragorn fulfills the role of king by taking Paths of the Dead and reappearing in Gondor.
The water of the fountain called the Mirror of Galadriel functions as a symbolic baptism while lembas waybread given to Elves recalls God's gift of Manna to the Israelites during their exodus to the Promised Land at Exodus 14.
Brian Rosebury interprets Elrond's statement as implying an Augustinian universe created good while Jesuit John L. Treloar comments that Ringwraiths bring four evils into the world: conquest war famine and death.