The three denials
What difference does it make that the maid is the first to give Peter away? The men could have recognized him instead. Perhaps this happened so that we may see that the female gender also sinned by killing the Lord, so that His passion should also redeem womankind. A woman therefore was the first to receive the mystery of the Resurrection and to obey the commands (John 20:11-18), so that she abolished the old error of her sin.
Why did the Lord chose Judas if He knew that he was a traitor?
Judas chosen among the twelve apostles, and had charge of the money bag, to lay it out upon the poor, that it might not seem as though he had betrayed the Lord because he was not honored or in need. Therefore the Lord granted him this office, that He might also be justified in him; he would be guilty of a greater fault, not as one driven to it by wrong done to him, but as one misusing grace.
The Holy Eucharist is the first, most important, and greatest miracle of Christ. All the other Gospel miracles are secondary. How could we not call the greatest miracle the fact that simple bread and wine were once transformed by the Lord into His very Body and His very Blood, and then have continued to be transformed for nearly two thousand years by the prayers of priests, who are but simple human beings? And what is more, this mystery has continued to effect a miraculous change in those people who communicate of the Divine Mysteries with faith and humility.