On one hand, the Trinity doctrine makes perfect sense with respect to many passages in the Bible. The creeds were an attempt to quantify the beliefs of Christianity and while the Apostles' Creed is fairly straight-forward, the Nicene got messed up. That happens when theologians start debating what is and what is not with respect to religion. It becomes a man-made thing and out of the Nicene Creed, which has enough problems that later creeds were written in an attempt to help people understand its principles (they only made things more confusing), came the Trinity doctrine.
Even today, there are a number of different view of this doctrine and some are diametrically opposed to each other.
Now add Biblical proof and that is where the whole thing gets into trouble. There are a number of instances, where there is a clear separation of the Father and the Son (and in some instances, the Holy Spirit). The first and foremost is the baptism of Jesus, wherein Jesus was very much physically present in the form of a man, the voice of God (the Father) was heard from heaven and the Holy Spirit was witnessed as an entity of some kind that descended as a dove would descend. When I asked about this, one of the responses was, and I quote: "Do you believe that God cannot be a ventriloquist?"
My reaction was, why should he be a ventriloquist? Do you believe there was no God in heaven while Jesus was on the Earth for 33 or so years? Was there no God in heaven while Jesus was a baby or growing up?
That only adds to your question about Jesus praying to God, not to mention the stoning of Stephen, wherein he testified that he saw the heavens open and Jesus Christ standing at the right hand of God! How can separate beings be the _one_ God in any kind of metaphysical sense? The later creeds of Catholicism tells us that God cannot be separated. And yet, in the scriptures there is ample evidence that during those 33 years and beyond, that Jesus and God were not the same being?
The answers that are given are not very satisfying and never have been to this kid who was raised Episcopalian. I rejected the concept of Jesus and "Our Father, which art in heaven" are the same person, being, essence, _or_ God. To me, it has always been clear that Jesus and God are two separate beings.
I go along with Paul, who wrote to the Corinthians (KJV): 1 Cor 8:5 For though there be that are called gods, whether in heaven or in earth, (as there be gods many, and lords many,)
6 But to us there is but one God, the Father, of whom are all things, and we in him; and one Lord Jesus Christ, by whom are all things, and we by him.
By using the conjunction, and, Paul clearly separates the Father and the Son. Why the Trinity exists in light of this scripture alone, not to mention the other examples given, is beyond me. It is clearly teaching another Gospel and not the one the Apostles taught. (TD's expected.)
Add: Wow. After 22 minutes and you aren't getting much in the way of responses from Trinitarians. That says a lot, doesn't it?