No, God did not know, predestine or desire the fall of Adam and Eve. He knew of the possibility, but not the outcome, because it depended on human choice. Adam and Eve were created sinless, not perfect, and I think those terms are often confused. Although the Eden story on face value has been interpreted to mean that Adam and Eve were created full grown, I believe they had to start out as infants, like anyone else. They had a process of maturation to go through. Perfection, was their goal, meaning perfection of their capacity to love God and each other, when they reached both physical and spiritual maturity. It is equivalent to "be fruitful" in Genesis 1:28.
The Tree of the Knowledge of Good and Evil is a symbol of Eve and the fruit of the tree is a symbol of her sexual love. The prohibition on Adam and Eve not to eat the fruit was necessary only until they reached maturity and perfection. Then Eve would have become a Tree of Good. The prohibition on eating was necessary during their immaturity because the power of misdirected love could sever their relationship to God during their growing period. Eve became the Tree of the Knowledge of Evil, by succumbing to the temptation from another spiritual being, jealous of their future position as God's son and daughter. Through the fall, the premature partaking of sexual love, this spiritual being could control Adam and Eve and their descendants through the power of misdirected love.