Well, you are asking several questions here, and there are some other factors.
o Did Adam have an independent will?
o How did he form his fact base about his environment?
o Did Adam have a rebellious spirit?
o What did Adam know about "death"?
o Did Eve have a free will?
o How did Eve form her fact base about her environment?
o Who was supposed to tell Eve about the tree of the knowledge of good and evil? The Jehovah Elohim? Adam? The serpent?
o When did "death" enter the kosmos?
o After eating of the tree, what happened to Eve?
o What did Adam and Eve know about three kinds of life and three kinds of death?
etc., etc.
That whole panoply of philosophy I did not ask about. I'm feeling that by your question above you're side-stepping my query, about your position that Adam rebelled, which was:
Can you prove that? Or did you just assume that?
(I can't do anything more on this today -- take your time)
All we know is what God has told us about this situation which is that He gave Adam and Eve only one rule that He expected them to obey. He gave them that rule so that they would have a mechanism of free will - so that they could rebel against them if they chose. As we know, God does not force anyone to love Him or accept Him, and as Adam and Eve were placed in Paradise, the Tree was the only way that they would have a way to exercise their free will.
We know that God walked with them in the Garden; we know that they communicated with Him on a one-to one basis; we know that He was always available to them; and we know that they were well aware of the one rule that He had given them.
I don't think that Adam or Eve were made with a rebellious spirit but they did have free will by virtue of the fact that God provided them with a way to make a choice. When Eve was deceived and made the choice to rebel and approached Adam, he also had the choice to rebel or turn to God, with Whom he had ready contact, for help and he made the choice to break the one rule he and Eve were given.
So, given that God provided Adam and Eve with a mechanism to make a choice to rebel against Him or not, and given that they had God in Person, physically, right with them in their midst and they had immediate access to His help, then I believe that God Himself has made the point in this account that Adam and Eve did indeed freely choose to sin and rebel and disobey and, as a result of that choice, and as we know from Scripture, bring about the fall of man.