(1) Why was it necessary for Jesus to die on the cross?
Let me try a very short answer which I am sure will only produce more questions, but anyway. There are other parts of this web page which talk about the cross extensively, please have a look at the Cross of Christ page.
Each of my statements would need the backup of references in the Bible, (given in the reference above) but you wanted an explanation in my own words.
1) The Bible is full of strong statements about the holiness of God.
2) God made it very clear, before the first sin, that the consequence of sin is death, and that is reiterated throughout the Bible.
3) Sin is rebellion against the highest authority. It is an offense against God's holiness and right to institute all laws. It is basically saying that we know better what is right and wrong and we disregard God's authority.
4) When God doesn't want to dilute the seriousness of his commands by "just forgiving it without penalty" which would compromise his own holiness, then transgression has to find its punishment.
5) But God is not only holy and just, he is full of love and does not want that any should perish.
6) Even in our court system, if a person is fined 500,000 dollars and unable to pay [we are fined (spiritual and physical) death - but if we have to pay that is the end of us] then it is acceptable if some other person comes in and pays the fine for the person. [we don't have the allowance for for substitution in the case of a life sentence for murder, but in case of a monetary fine it is usually not asked where the money is coming from.
7) God's holiness and justice demands punishment of sin according to its seriousness of offense. God's love and mercy moved him to pay himself for it, since he doesn't want to destroy us although we would have deserved it.
8) Jesus death on the cross is the substitutionary payment of all of sins death penalty of mankind. If I accept the substitution, then I am free. If I insist to face God on my own terms, then I will have to bear the just condemnation of my sin myself.
9) Why the cross? God could have done it different ways. Why crucifixion and not stoning? This question is not answered. The why of the death of Jesus and its meaning and effect is clearly answered in the Bible. This shameful and horrible death is appropriate for the shamefulness and horridness of the sin punished. And the earlier prophets have predicted much of the cross in their writings. You might want to check out my article at the above mentioned web page.
The same holds for questions on the Biblical evidence for all these claims.
There you will also see that the Gospel = the "message of Christ crucified and raised"
(2) Could a mere human have served the purpose?
"No", because there was no human who has not his own sin to bear. Only one without sin could be the substitute for others. Only if I am not already in debt myself and bankrupt, can I pay the penalty for any other. So, "theoretically" if there had been a sinless human being who was nothing but a human being, then yes. [at least that is how I see it]. But there was none, because all have sinned and have defiled themselves with their rebellion against God in many small and big disobediences. It is very much like the story of Abraham, who is called to sacrifice his son, but then God himself provides the substitute in the place of the one who was to die. In the same manner, Jesus is the substitutionary lamb who died in our place so that we may live.
So: "Yes", a mere human would have been enough, but there was none. The problem is not in being human or not, the problem is in purity or rather the lack of it in any human.
(3) What portion (molecule, percentage, etc.) of God died on the cross? If only the human aspect of Jesus "died," what is the big deal?
God is spirit, and not matter. God has created molecules, but he does not consist of molecules. And it does not make sense to talk about percentages of the infinite.
Well, God can not die by definition. But the problem is that you can not "neatly" separate God and man in Jesus. Jesus is (God who became) man, real man, not just a fake appearance of a human being. And this MAN Jesus died. I don't say that is an easy concept. I have not "invented" it. That is what is revealed in God's Word. But I can try to understand it better and better by thinking about that which is revealed.
The big deal is, that he died for me so that I might have forgiveness of my sins and be reconciled with the Holy God.
(4) If a mere human could not serve the purpose, and no portion of God died on the cross, how could the goal be accomplished?
I think the question has been answered in the above. The perfect and pure human being Jesus [who happens to be God incarnate] was serving the purpose and served it perfectly.
I hope that these explanations do help at least a bit.
Please keep in mind that I am a fallible human being and I am trying to answer to the best of my knowledge -- which is not perfect. I do not claim to be right in all I say. I am always glad about corrections to my answers or a renewed question that asks for more clarification where I stayed unclear.
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