You are asking some really big questions here. I am answering both of these in much detail in the class on Christian Theology I started yesterday. You can join us Saturdays at 9:00 Pacific Time the next three Saturdays. www.bakersfieldchurchofchrist.com or zoom 342 225 5971 pswd 857096.
But let me give you very brief introductory answers to your questions. These answers will be abbreviated and may not completely satisfy.
1. To start with, the idea that the Father sent his Son to die in order that we could have salvation, redemption, justification and forgiveness of sins is not clearly logical by human ways of thinking. As I said in our class yesterday, God’s plan for redemption of humanity is a mystery. This is what we are told in the Bible. The biblical fact is that Christ died for our sins (1 Corinthians 15:3). This was both because of our sins and so that our sins could be forgiven. This “message of the cross” is a mystery and it is a stumbling block to the “wise” of the world (1 Corinthians 1:18-21). Again, this plan to redeem us through the sacrifice of Jesus is a deep mystery (Ephesians 1:7-10). His death brought redemption and unity between mankind and God. This mystery is what brings Jew and Gentile together (Eph 3:3-12), and allows us to approach God without the stain of sin.
Having told you redemption through the death of Christ is a mystery, let me try to give some sort of biblical account of how and why God chose to save us this way. The wages of sin are death (Romans 3:23). Nothing good we do solves this problem. We were “dead in our sins” (Ephesians 2:1) with no solution, at least as far as what we could do ourselves. God chose to fulfill the Law and the Prophets through Jesus (Matthew 5:17). Jesus took the penalty that God’s justice required so that we would not have to pay the ultimate price for our rebellion and sin. Again, this is a mystery–why God chose this path, but it is what he chose. The best statement of this idea in the Bible I know is in Romans 3:20-26. Here you will see God’s pronouncement that we could not be declared right before God based on our own works. Good work does not cancel out the consequences of sin (v. 20). As humans, we understand that part. But God provided the solution, so that he could be just (hold sin to account), but also to justify (forgive) us (v. 26). He did this by substituting the death of Jesus–his sacrifice–so that we would not be held to account–so that we could be justified.
Could God have done this another way? I hate to put it this way, but I guess you will have to ask God. This is the path to justification he chose. Is it “logical?” Not to me, but I accept it because it comes from God, our Creator, to whom we will give account.
2. Speaking of Trinity, talk about mystery! I talked about this in my class yesterday. Perhaps you can go to my website and listen to the class and look at the notes. The trinity is a mystery. The Bible is absolutely, without any doubt, clear that God is one. There is one God. Yet, we have John 1:1. In the beginning was the Word (referring to the Son). The Word was with God, and the Word was God. How can this be? The mystery of what we sometimes call trinity (a word not in the Bible) is about relationship. God is inherently a relational being in his very nature. The mystery of trinity is about God in relationship within himself. The Bible tells us that the Son submitted to the will of the Father on the cross. “Yet, not as I will, but as you will.” (Matthew 26:39). The answer to this question, clearly, is closely tied to your first question. Did God sacrifice himself? I suppose we could put it that way, but I am confident that Jesus would not say it that way. God the Son offered his life, not to the Father, but so that we could be saved. It was the ultimate act of love, both of the Father and of the Son for us. Am I going to claim that this is logical? You can guess that I will not. It is a mystery, but it is a beautiful mystery, to which I submit myself. I cannot blame you one little bit for feeling that this concept is difficult to grasp or to accept, but it is what we learn in the Scripture–the Scripture which is inspired by God, as is clear from so much internal evidence, including the resurrection of Jesus, his miracles, and his fulfillment of prophecy. But that is another story.
Is the “trinity” a contraction? No. It is reality. Jesus is God (John 8:58-59 and many others), but Jesus is not the Father. It is a mystery, but it is reality, not a “contraction,”