GregorySon -
(1) What part of the term "immortal" and the concept of Immortality do you not understand? By definition, that which is immortal cannot die. The term "immortal death" which you use is an oxymoron; it makes no sense.
(2) Adam did not POSSESS a soul; rather, Adam WAS a soul. The English term "soul," like the corresponding Greek term PSUCHE, means "being" or "entity" or "creature." But the being or creature is not a "LIVING soul" until it is animated by impartation of the Spirit of Life. The the Spirit of Life simply animates the individual; it does not correspond to the concept of the Immortal Soul.
(3) That which the Lord God breathed into the nostrils of Adam was not an "Immortal Soul"; rather, it was the "Spirit of Life" -- a spirit which the Lord imparts in order to animate creatures of the Natural Realm. In the progeny of Adam, the animating spirit is imparted upon the first inhale after birth; upon death, it returns to the Lord, Ecclesiastes 12:7. Inasmuch as the Greek term PNEUMA is used for wind or breath as well as for spirit, the Spirit of Life sometimes is termed the Breath of Life.
(4) In a figurative sense, separation may be construed as death. But separation is NOT the death of which the Lord warned in Genesis 2:17. The immediate context makes clear the fact that the death in view is physical death, which ultimately results in utter annihilation: "In the sweat of thy face shalt thou eat bread, till thou return unto the ground; for out of it wast thou taken: for dust thou art, and unto dust shalt thou return," Genesis 3:19.
(5) If you take the trouble to think about it, you should be able to see that, by his argument that the Wicked and the Unbeliever are tortured for evermore in Hell, the Protestant is asserting that the Wicked and the Unbeliever have "everlasting life"; after all, it is impossible to inflict torment upon the dead. Concerning the state of death, Job observes: "There the wicked cease from troubling; and there the weary be at rest. There the prisoners rest together; they hear not the voice of the oppressor. The small and great are there; and the servant is free from his master," Job 3:17-19. Thus, the concept of Everlasting Torture demands the concept of the Immortal Soul. But, both the concept of the Immortal Soul and the concept of Everlasting Torture are foreign to the Scripture; they are pipe dreams which exist only in the imagination of the Protestant and the Talmudic Jew.
(6) If that which you term "death of the Soul" truly was the penalty of which the Lord warned Adam in Genesis 2:17, then the concern of the Lord regarding the fruit of the Tree of Life would make no sense: "And the Lord God said, Behold, the man is become as one of us, to know good and evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever: Therefore the Lord God sent him forth from the garden of Eden, to till the ground from whence he was taken. So he drove out the man; and he placed at the east of the garden of Eden Cherubims, and a flaming sword which turned every way, to keep the way of the tree of life," Genesis 3:22-24.
(7) You argue on the basis of theology; but the Christian Faith is not based on theology. Rather, the Christian Faith is based upon the Scripture. That which you term "Soul Death" is an invention of the Protestant; it is a concept which is foreign to the Scripture. Unless and until you can argue from the Scripture, citing book, chapter, and verse, your claims are nothing more than baseless speculation. Moreover, they are directly contradicted by the plain teaching of the Scripture.
RLH
25 February A.D. 2020