These are good questions, and they are deep. While the questions may seem simple, there is much to understand before it makes sense. And I'm afraid there are at least a few basic things that are different between our Faiths that may make it difficult for you to see what is being conveyed here, but I'll try! I think others will, too.
So first of all, it is indeed puzzling that in the OT G-d could forgive sin, even at such a heinous level like what King David committed. Yet your background also teaches He is Most merciful? Yet what we see, is that forgiveness rests on Christ's finished work on the Cross.
We see that He went to "the spirits in prison," and preached to them after He died by crucifixion. We see that the gates of hell did not prevail, and that Jesus conquered death! And He brought those in sheol that believed His Gospel with Him. So in this way G-d's forgiveness through Christ, transcends time. Does Islam also teach that G-d is not only eternal but unaffected by time, knowing the end from the beginning?
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Different subject:
how can Jesus "taste death for every man?" (And woman, and child) The theological term is "expiatory power," but even without that we see the concept presented over and over throughout the Scriptures. Take David and Goliath for example. Why did those two fight? It is the same concept. Since Goliath lost, it is presumed that every Philistine would lose to every Jew, and more humane that only one need to actually fight and die.
Neat trick, huh? Even the Jewish High Priest saw how it would be more expedient for one man to die for the sins of the whole people ...
There are many MANY different ways of understanding this! Scripture is chock full of them. I do really believe that we could spend the eternity of eternal life looking upon this as it is, and not only never be bored but be thoroughly and ecstatically consumed with worship. Yet in this life we are limited in our understanding of it. While it is nice when G-d grants us a moment to see more clearly, our Faith still comes down to humility and obedience. I suspect that is not too different from your experience?