I'm confused....
First you say that children don't inherit their parents sin. Then you say we inherited Adam's sin. Did King David's son inherit the Original Sin and therefore is condemned as an unbeliever?
Then you quote King David who also said this about his son who was conceived in literal sin. The child died a physical death by God's hand. But.....
"2Sa 12:22 And he said, While the child was yet alive, I fasted and wept: for I said, Who can tell whether GOD will be gracious to me, that the child may live?
2Sa 12:23 But now he is dead, wherefore should I fast? can I bring him back again? I shall go to him, but he shall not return to me.
2Sa 12:24 And David comforted Bathsheba his wife, and went in unto her, and lay with her: and she bare a son, and he called his name Solomon: and the LORD loved him."
Does scripture say those Amalekite babies will stand at the White Throne judgement?
Did God saved His own when He had them attacked by the Assyrians or the Babylonians?
Any time there is temporal war, innocents die temporal deaths.
I didn't say we inherited Adams sin. I said we are all born with a sin nature. Adams sin was imputed, or other words, Adams sin has attributed to everyone being born with that same attribute.
I never said anything about King Davids first son, but did give scripture about his other son Solomon that he was of God even before the womb, Judges 13:3-5.
Yes, I believe the children of the Amalekites and the Egyptians plus the babies of Sodom and Gomorrah or any other seed of Satan will go to the lake of fire as God judges the secret intentions of the heart. There are two seeds with one being the seed of promise and the other the seed of Satan. I'm not talking about the spawn of Satan, I am talking about the darkness of an evil heart and the seed or offspring that comes with it.
Yes I agree anytime there is war many innocent die as in the seed of Abraham, but also those who are not innocent as they die in the seed of Satan. Only God can judge those deep things of the heart that are kept in secret.