Where's the Missing Piece?

I've been doing a parallel study of the Gospels, a task I've desired to complete for some time. I have learned so many new things from stories that I thought I knew so well. I'm eager to know more and hear perspectives from others that I may not have considered or known.

1. Matthew, Mark, Luke, and John may not all have been disciples of Jesus. In fact, there is a possibility that they all  may not have known each other directly. Different theologians and historians have found evidence that speaks for both ideas. I've had pastors from multiple churches teach different perspectives as well.

2. All four books that are Gospel are written for different purposes and with a different audience in mind. Matthew wrote to the Jews, specifically addressing prophecies of the Old Testament. Mark wrote to the gentiles and focused on the power of Jesus as God, Luke wrote to the Greeks and emphasized Jesus and his life's ministry. John is the odd ball out- the book is written from an entirely unique perspective and with a different voice.

My questions as I'm studying:

1. Why did each person choose to include what he did in his book? Why does Luke have so many details about the birth of Christ and John is the only gospel to reference Jesus' first miracle?

2. If the authors of the Gospels did  not know each other or possibly Jesus directly, how are there certain quotes that are almost verbatim in multiple Gospels? Is there a source that they may have used to cross reference? 

I do not claim to be an expert in any of these things and I recognize that taking just one study guide as fact is ignorant. I'm excited to learn more!