For a big part of it please see the link I believe I posted earlier in the thread.
Basically mankind lived in a state of innocence, not sinless perfection. Adam and Eve decided, for everyone, to have for themselves the power to determine what was good and what was evil. Once they got it they found out that they were evil! They were self-condemned even before the Law of Moses. That’s why it say “nevertheless death reigned from Adam till Moses”. I could go on but I have already written out an explanation for these verses in great detail in the link.
Micheal Heiser describes Adam’s act as producing the conditions which led to everyone being a sinner. Heiser’s view, which as it turns out aligns closely with my own even though he has not yet considered the two-population model (all the more amazing to me because I never even began to question it until I saw the two-population model), is described in more detail than most would want to know here…
@Ashwin_s I think the answer and links above are also instructive to our dialogue. I’d say the desires becoming corrupted (your #3) is a process because our flesh pulls us one way but our desire for God pulls us another. Thus one can be tempted by sin even without the desire for it in our inner man. This was the condition I believe applies to all of us, even Christ in the incarnation, but I would not call it a “sin nature” until it actually becomes a part of our nature. Which it does for all of us but him! Once our will starts to make peace with #2, we get a sin nature.