12. What is the meaning of the Incarnation? Was Joseph the biological father of Jesus?

As to your question about Joseph being the biological father of Jesus... The Church's clear teaching, as expressed in the Catechism of the Catholic Church, and in Tradition and Scriptures, is that Jesus was conceived miraculously by a special divine intervention (C 484-507). For example, The Catechism states: "From the first formulations of her faith, the Church has confessed that Jesus was conceived solely by the power of the Holy Spirit in the womb of the Virgin Mary, affirming also the corporeal aspect of this event: Jesus was conceived "by the Holy Spirit without human seed" (C 496).

I would recommend that you read these paragraphs in the Catechism. They point out that we are dealing with a miraculous intervention of God, not a legend or theological construct. The theological implications of this belief are spelled out in the Catechism. You might also want to read C.S. Lewis' reflections on the Incarnation in his book, Mere Christianity.

A few other points: it is by no means certain that Mary was 14 years old when she became the mother of Jesus. This is a presumption with no particular basis in history. All women do not marry at the same age today, and we can be sure that all women did not marry at the same age in Jesus' time, especially in a small village like Nazareth. We should not assume that she was a naive little girl. St. John Chrysostom's explanation that an angel had to calm her is a pious legend without any basis in fact.

The fact that Jesus was conceived in the womb of Mary by the power of the Holy Spirit was the greatest miracle in the history of the human race. Jesus is uniquely God and human, and the Catholic Church has always believed that he was conceived by God's power, not by human intervention. We cannot understand this, but it is certainly not beyond the power of God to accomplish. It results from the incredible Love God has for us.