Dr. Joye Pugh - Symbology of the Garden

Was eating of the fruit within garden paradise symbolic of an act of sexual lust which led to the impregnation of Eve with the firstborn son of Lucifer, Cain? Did this act result in the loss of immortality and incarnation into the flesh for humanity and future progeny? Is this why the Lord told Adam he would have to now work the ground to bring forth sustenance for his children? And is this why the Lord cursed Lucifer and told him that, "And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel?"