I do not believe you, I, or anyone else alive today can speak as to what Adam knew or did not know concerning the difference between the tree of life and the tree of knowledge of good and evil.
As far as what is the difference between the "Book of Life" and the "Book of knowledge of good and evil"?
I know what God's Word tells me about the book of life.
As there is no reference to the "Book of knowledge of good and evil", God's Word is silent. So I know nothing concerning this "Book".
Again, what I know about the "Book of Life" is what is written in Scripture and what I know about the "Tree" is what is written in Scripture.
I would offer the book of life is where God wrote the names of those all who he intended to give the gift of faith to. This is in respect to the lamb of God slain from before the foundation of the world. The tree of life could represent the idea of the family tree . The tree of life, Christ that we eat of is the kind of spiritual food the disciples knew not of. The food of doing the will of another as we were designed to do. "Our free will to do the will of God previously having no faith. Not being in bondage to the god of this world. Again we were not created as free agents it goes against the original design.
The books will be opened I would suggest two.
One with all the names he would bring into this corrupted world and the other in respect to the lam of God .When compared if any man name is not found in the latter book we understand they had no faith needed to believe God.
Revelation 20:12 And I saw the dead, small and great, stand before God; and the
books were opened: and another
book was opened, which is
the book of life: and the dead were judged out of those things which were written in the books, according to their works.
I would offer whenever we hear the word of God, mixing faith (believing God not seen) in what we do hear, we have in effect eaten of the tree of life.
Revelation 2:7 He that hath an ear, let him hear what the Spirit saith unto the churches; To him that overcometh
will I give to eat of the
tree of life, which is in the midst of the paradise of God