Alter2ego,
Thank you for posting. Before getting to answer your questions, I would like to mention to all that the Bible Basics Site and Forum do not promote controversial discussions. The Bible encourages us to stay away from vain arguments as well. However I would like to answer your questions from my experiences in knowing God as Father, Son and Holy Spirit in my life and with material collected from discussions with a learned Bible teacher. I would like to mention that I have no intention to carry on with any further arguments on this subject. Such arguments are beyond the scope of the Bible Basics Forum.
Before going forward, I would like to mention that God the Father, God the Son and God the Holy Spirit have existed much before you and I were born. They are not split up expressions of who God is as you mention in your post. Our limited human intellect can never entirely fathom the mystery of Trinity. That's because God is God with no limitations where as man is only man with a very meager understanding especially about God. Man's inability to comprehend can and will in no way change who God is. As mere mortals we say 1+1+1=3 however with God, 1+1+1=1 God! This might baffle the human mind but that does not change the truth about God.
1.There are certainly Bible passages that clearly set forth the Trinity. First in Genesis 1:26 God says, "..Let us make man in our image, in our likeness,...." Here we find that God uses the word 'us' and not 'me' clearly showing that God the Son and God the Holy Spirit were also actively at work in creation. The second reference I would like to mention is from Matthew 3:16-17 which is an account of the Baptism of Jesus. Here we clearly see Jesus, God's Son being baptized, the voice of the Father who says, "This is my Son, whom I love; with Him i am well pleased" (Vs 17) and the Holy Spirit descending on Jesus as well (Vs 16). Another Scriptural reference is from Ephesians 1:3-14. The Apostle Paul clearly sets out God the Father's plan to redeem man through the atoning sacrifice of His Son Jesus and the guarantee of this salvation through the seal of the Holy Spirit.
2.You say that there were pagan trinities much before Jesus came into the world. Here I could like to remind you of the Genesis passage which shows that God the Father, God the Son and God the Holy Spirit were at work in creation which happened even before any of these pagans or their customs were born!
3. Anyone who truly finds the God of the Bible finds God the Father, God the Son and God the Holy Spirit. That is the essence of Christianity itself. I can say this because I have experienced it myself. The disciples witnessed the baptism of Jesus and it is their account that is mentioned in the Gospel passages. The disciples became Apostles and so there is clear evidence to prove that the disciples did affirm and preach God the Father, God the Son and God the Holy Spirit. The Ephesians passage mentioned above shows how Paul even wrote and taught about the unity in the working of God the Father, God the Son and God the Holy Spirit. The main purpose for Jesus to step into the world was not to teach or preach Trinity but to lay down His life for fallen mankind so that man can be reconciled with God. This does not mean He disbelieved Trinity or disapproved of it or belittled it in any manner. He came for a purpose and He stuck to it. Jesus is One of the Persons in the Trinity and there was no need for Him to vocalize it. His life proved His position sufficiently.
4. For this question, you really must provide more material to support your view that the Trinity teaching came up only after Christ's resurrection.
5. There is no direct mention of the words Trinity or Godhead in the Bible. These words were coined by Bible teachers to help understand God as Father, Son and Holy Spirit with ease. It is more of a common term to help explain rather than a special word pulled out of Scripture.
I hope these answers have helped you. It is my hope that at the Bible Basics Site and Forum we always only explore the truth of God's word and nothing more.