There is much here. Yes, Eve was the one deceived, whereas Adam chose to sin with his eyes open. Because of this they spiritually died. They were put out of the garden, as you say they were separated, but they also began to physically age and die, and both did die a physical death, another thing that changed was their nature. This changed nature- the sin nature was what has ben passed down to humanity since. Remember, they didn’t have children until after their fall.
All people since have been born with this fallen sinful nature. Jesus is the exception to this. He was born with the same nature that Adam and Eve were created with. I could go in depth about why I believe this to be true, but consider the one major difference which we all believe about Jesus, namely that he was born of a virgin. I don’t believe that God did this just to create a miraculous deed though it certainly was. I believe God did this because only by removing the male from the reproductive process could an unfallen nature be produced in the female womb. Again, I could go in depth, but I believe the sin nature is carried in the blood of men ( perhaps in both men and women) and passed on that way. ( My beliefs here are not exactly spelled out explicitly in scripture, but alluded to in scripture and other things I have studied.)
Here’s some things to consider regarding blood:
It is crucial in the atonement process both in the OT and in Christ’s death. His blood HAD TO BE SHED. It’s use in the sacrificial service was very meticulously specified by God. And God forbade the drinking of blood… Why? In medical science we know there are several types of blood. The types are so different that getting a transfusion of the wrong type can be fatal to a person, yet a mother can carry a baby with a different type of blood in her womb and not be affected! That’s because the mother’s blood never mingles with her unborn child. God could create a human child in the womb of a mother with a perfect untainted nature and it’s blood would not be affected by sin…
I will continue this line of thinking in another post…