Jesus did, in fact, claim to be God/Son of God. Some examples are listed below:
-Jesus said to them, "Most assuredly, I say to you, before Abraham was, I AM." John 8:58 (Jesus knew that the Jews would understand this as a clear reference to God in the burning bush, speaking to Moses).
-"I and My Father are one." (John 10:30)
-When Jesus heard that, He said, "This sickness is not unto death, but for the glory of God, that the Son of God may be glorified through it." (John 11:4)
-Jesus said to him, "Have I been with you so long, and yet you have not known Me, Philip? He who has seen Me has seen the Father; so how can you say, 'Show us the Father'?" (John 14:9)
-Simon Peter answered and said, "You are the Christ, the Son of the living God." Jesus answered and said to him, "Blessed are you, Simon Bar-Jonah, for flesh and blood has not revealed this to you, but My Father who is in heaven." (Matthew 16:16-17)
-But Jesus kept silent. And the high priest answered and said to Him, "I put You under oath by the living Hod: Tell us if You are the Christ, the Son of God!" Jesus said to him, "It is as you said. Nevertheless, I say to you, hereafter you will see the Son of Man sitting at the right hand of the Power, and coming on the clouds of heaven." (Matthew 26:63-64) (obviously, Jesus equated the phrase, "Son of Man", with "Son of God", with the former emphasizing the fact that Jesus was fully human, while also being fully God.)
Interpreting Jesus' response to the rich young ruler with the above verses, which clearly demonstrate that Jesus did claim to be God, it is reasonable to infer that the young ruler did not believe this, and Jesus, knowing this, therefore asked, Why do you call Me good, when only God is good.
As for the confusion about the Trinity, When the Bible says that there is only one God, the word "one" being used in these places is being used in the sense of "one cluster of grapes"; that is, there are multiple grapes, but only one cluster. So also God is one God in three Persons.
God is the Father of Jesus in that He is the source of Jesus, Jesus being His manifestation. You see, God, being omnipresent and eternal, cannot be detected locally or temporally in any way unless He has some way of manifesting Himself to us. Jesus (God Incarnate) is this manifestation. "Not only must the invisible and inaudible God be seen and heard objectively, however, He must also be experienced and understood subjectively. The life of the creation must be maintained in vital union with that of the Creator. The Spirit of God must move over the creation and must indwell it and empower it. The activity of the Spirit is distinct from that of the Son and from that of the Father, and yet is indissolubly one with both." (H.M. Morris, "Many Infallible Proofs" 115).
Jesus became human so that He could, being God Incarnate, live a perfect life and, being innocent, take the punishment we all deserve for our sins on our behalf, so that all who see Him (in faith) and come to Him, turning away from their sins, asking Him to pardon them from their sins, can be forgiven.