I hope I understand your question correctly, in that you find confusion in the part about Adam introducing sin into the World; and the part about death reigning over all people until Moses introduced the LAW.
First of all we need understand Adam's disobedience. Adam's sin of disobedience was Intentional.
Genesis 3:6 KJV And when the woman saw that the tree was good for food, and that it was pleasant to the eyes, and a tree to be desired to make one wise, she took of the fruit thereof, and did eat, and gave also unto her husband with her; and he did eat.
Gen 3:17 KJV And unto Adam he said, Because thou hast hearkened unto the voice of thy wife, and hast eaten of the tree, of which I commanded thee, saying, Thou shalt not eat of it: cursed is the ground for thy sake; in sorrow shalt thou eat of it all the days of thy life;
God did not tell Adam that he hearkened to Satan as had Eve; but instead had Harkened to Eve. Therefore, Adam was not deceived by Satan and was fully aware that he was disobeying God's word. That fact will be of importance when we get to the part about being like Jesus. So now let's take a long look at the part about sin not being levied until the law. Until the arrival of Jesus, God had only given his rules to only two men Adam and Moses. Without rules one cannot be charged with disobeying. So when Paul says that death reigned from Adam to Moseseven unto those who had not sinned as Adam had; All of those people who had not intentionally disobeyed God also suffered death; though they were sinless, as there was no prohibition other than not to eat from the tree of the knowledge of good and evil.
That all changed after God gave Moses the ten Commandments. Now God had decreed eleven rules to follow. Therefore, when one of those rules was broken the person was now committing the same sin as Adam that of intentionally disobeying God. Those who had not intentionally sinned had not lived faultless lives, indeed many had committed acts such as Cain killing Abel, but until the ten Commandments were given there was no rule about killing.
If I have misinterpreted your question please let me know. As far as your last paragraph it is the belief in Salvation that is the basis of Christianity, and the hope of eternal life. Otherwise After death there is nothing, and The soul does not exist, we simply die and are gone.