Alright, I will try to answer your questions.
1. You are asking about God the Father: He seemed to have committed a crime by letting Jesus die/killing him on the cross. And since God the Father is God, part of the Trinity, then that would make the Trinity sinful. That's a legitimate question you have here.
- God the Father did not sin in letting Jesus die/killing the Son. I will give you a simple example: This summer my roommate left the apartment for two weeks. She had a fish in the apartment and she asked me to feed the fish while she was away. So I agreed with her, I willfully feed the fish, so that it would not die. It's not a very good example, but in the same way, God (Trinity) knew that we were in great need, not of food (like the fish in my example), but to be saved from hell because of our sins. There was only one way for us to be forgiven by God and saved from hell: That a perfect human being die on our behalf and pay the consequence of the sin of the world. But who can do that? Who is perfect with a righteousness equal to God? Only God Himself. And who can die and bear the condemnation of all human beings? Only God can do that, no one else. So God the Father sent God the Son into the world to die for us and be resurrected to life again. It is true that the Father "sent" the Son, but it is also as much true that the Son "willfully" died for us. Like in my fish story, my friend asked me to feed the fish and I willfully fed the fish so it would not die. I had to get up every morning and feed the fish, even though sometimes I didn't feel like it. I know it's not a good example but I hope it helps you understand that the Father and the Son together planned our salvation and the Son wanted to give his life for us, the Father did not force him to die, Jesus wanted to die for us. Here are a few verses that tell us about this truth:
Those are the words of Jesus recorded by John:
"I came that they (people who would believe in Jesus) may have life and have it abundantly. I am the good shepherd. The good shepherd lays down his life for the sheep... I lay down my life that I may take it up again. No one takes it from me, but I lay it down of my own accord. I have authority to take it up again. This charge I received from my Father." (John 9:10-12, 17-18)
Jesus always said that the Father had sent him to die (lay down his life), but Jesus also always says that he himself wanted to lay down his life and die for us, knowing that he would take it up again (raise from the dead). Jesus says in this passage that he had the authority, the power to either lay down his life and to take it up again, and that was something the Father had told him he could do. Thus, we cannot say that God the Father sinned in sending Jesus to the cross, because Jesus willfully decided to die for us, he wanted to do it to please the Father and because he loved us. The Father did not force the Son to die, on the contrary, Jesus gave his life for us of his own accord, as he himself says. This is obvious also in the fact that Jesus could have sent hundreds of angels to fight for him when people wanted to crucify him, but he didn't do it because Jesus wanted to die for us, because he knew that apart from his death on the cross, there was no other way for us to be saved from hell.
When the Jews arrested Jesus and one of his disciples drew out a sword to protect him, Jesus said, "Put your sword back into its place... Do you think that I cannot appeal to my Father, and he will at once send me more than twelve legions of angels?" (Matthew 26:52-53). So Jesus had the power to stop the Jews from arresting him, but Jesus wanted to go to the cross.
God did not commit a sin by letting Jesus die on the cross since Jesus willfully gave his life for us.
2. You say that because the Son cried out "My God, my God, why have you forsaken me" on the cross, that means that there is a contradiction because Jesus was willing to "drink the cup" of God's wrath.
- I personally don't see a contradiction in these two statements of Jesus. As I wrote in a different message, Jesus had to go to the cross, still he went of his own accord, and he knew that on the cross, he would have to "drink the cup" of God, which basically is the wrath, the condemnation of God, that we all deserve for our sins. Jesus knew that during his life and he purposely went to Jerusalem to be arrested and then killed so that he would drink the cup of God's wrath so that all who would later on believe in him wouldn't have to drink it themselves. Now when Jesus was on the cross, when God's condemnation of human sin fell on him fully, when Jesus "drank the cup" of God's wrath, then Jesus cried, "My God, my God, why have you forsaken me" not necessarily because he was actually wondering "God! Why have you forsaken me?!!!" but because he was experiencing for the first time, separation from God. God had forsaken him because Jesus was bearing the sins of the world and God cannot be in a relationship where the person is a sinner, because God is perfect and holy. So the Son, on the cross cried out "My God, my God, why have you forsaken me" not because he didn't understand that he had to drink this cup, but because he was experiencing something so deep and heavy, a total separation from God because he was bearing our sins, Him the Son of God, perfect in everything, He was being punished for us. We will never be able to understand the depth of the pain Jesus had to go through for us, not only on a physical level, but especially on a spiritual level. Because Jesus the Son was without sin and had always enjoyed a perfect relationship with God the Father and then, on the cross, all of the sudden, he experiences God's wrath for sins he hadn't committed. All that because he loved the Father and he loved us. What great love! What is more is that God rose the Son from the dead three days later and one day every knee shall bow to him.
Finally, you also said that you believe that none of the Bible writers saw Jesus crucified. Well, if you read closely in John 19:26, Jesus is on the cross and there, at the foot of the cross are the disciple whom he loved (this is believed by most scholars to be John), the mother of Jesus and other people (see John 19:25-27). So it is a mistake to think that there was none of Jesus disciples at the cross when he died. It is true that we don't know exactly who was there because the Bible doesn't tell the names of everybody who were there, but I don't see contradictions in the different accounts of the death of Jesus in the Gospels (Matthew, Mark, Luke and John). They are different accounts because they are told by different people (just think when different people see an event or a movie, they will all explain the event or the movie in different ways), but the accounts do not contradict each other.
Anyway, I hope this is helping you a bit, as I always say, I am only trying to help you understand what the Bible says, I don't have all the answers, only God does. Ask him to help you understand the Bible and His will for sending Jesus on earth. Can I pray for you?
Have a good day and ask more questions! Why are you interested in Jesus? Have you practiced religions before? Which ones?
Have a good day my friend,