The reason you don't have a teaching on the trinity is because there is none. All you post are bits and pieces of words and half verses and all taken out of context or from bad translations or not understanding how the words were used at the time they were written. Thomas is a great example...
Jesus is God's messenger/agent/representative (Jewish Law of agency - shaliah). We can clearly see this Jewish principle through the entire gospel of John. Jesus was sent by God (the Father) as God's messenger. Jesus was God’s representative on earth. God gave Jesus the right and authority to act in His name. And that is why Jesus declared that whoever receives him automatically receives God the Father, that whoever sees him sees the Father, that whoever believes in him actually believes in the Father who sent him and conversely, whoever rejects him rejects the Father who sent him (John 12:44-45; 14:7; 1 John 2:23).
It's therefore true that whoever sees the Son sees God the Father. However, there is another dimension to this mutual relationship between them. In the NT we read that Jesus as the Son of God is the image of the invisible God (Col. 1:15), he is the radiance of his glory and the express image of his nature/person (Hebrews 1:3), that in the face of Jesus Christ the glory of God can be seen (2 Cor. 4:6), that the Son came to reveal and show us God the Father (who is spirit and whom no one has ever seen - John 1:18), and therefore that it's in him that we can know God the Father and that he is the only "way" to the Father, that in his human body dwells the Father himself (Col. 2:9 - "all the fullness of the Godhead bodily") who acts through him. Therefore, it makes perfect sense that whoever sees and believes in the Son automatically sees and believes in God the Father.
This was also understood by the apostle Thomas (John 20:28 compared with John 14:5-9) who finally realized and believed that in Jesus he saw the one true God - the Father, who dwells in him and He is doing everything through His Son (including his resurrection). It's also our duty to realize that Jesus Christ is the visible image of the (otherwise) invisible God and that we can know the one true God - the Father and reach him only through His Son Jesus Christ, as the only way leading to God.