The verse says that by one man sin entered the world.
Because he was first. Thats logical. If you had be first, the sin would enter the world through you. Its nothing mysterious.
That refers to the first sin, which is the original, because it's the first.
But thats not the doctrine of the original sin. The doctrine of original sin is that we all sinned in Adam and therefore there is some generational guilt just because we are his children. That we bear his sin.
Your link hinges on the idea that one word has been misinterpreted by Augustine in one verse (Romans 5:12). (Think back to 1 Tim 2:13).
You did not read the link properly. The link was about the doctrine of the original sin - this doctrine is a wrong translation of Augustine. 1 Tim 2:13 just mentions the order of creation so it has nothing to do with it.
I'm not sure how we got to this place, I had a quick recap and it appears you were saying that Paul could quote Genesis as any other myth (you tied this in with something about long hair on men being a medical Greek myth).
Yes, its a funny story. In the times of Paul, it was a generally accepted fact that female's fertility is hidden in their hair. Therefore the longer hair they had, the more fertile they were supposed to be. It transformed into idea that hair are women's reproductive organ.
Therefore it was shameful for a man to have this women's reproductive organ (long hair).
Paul takes this obviously wrong idea and says "its what the nature teaches us".
I get it: evolution (theistic or otherwise) can only be incorporated into Christianity if we rewrite the Bible. This was pretty much what I was thinking. Thanks for your input
If you have some kind of anxiety imagining that not everything in the Bible happened in the physical world exactly as written, then the natural sciences are not for you, at the moment.
Later in your life you can base your faith on something more robust than just the literal reading of the English Bible. For example on the spirit in you, your own walking with God etc.
It will still be Christianity, but not the fundamentalist American branch of it.
Summary: Christianity is compatible with evolution (and other natural sciences like astronomy, physics etc.), because the basics of Christianity are very simple and the spiritual realities are more important than the physical one or than the ancient cosmology.
But the literal reading of the Bible or taking every word in the Bible as dictated by God, probably not. Its as incompatible as the ancient cosmology is incompatible with the ISS circling around our heads right now.