If the snake and Satan and the ground were cursed, then how is Adam not cursed since he comes from the ground? If a curse is something that can't be reversed, then how could even Christ reverse it with His death?
Mankind's eternal identity is not found in our flesh but in our spirit, as Paul explains in Romans 7:
Rom. 7:18 For I know that nothing good dwells in me, that is, in my flesh; for the willing is present in me, but the doing of the good is not.
Rom. 7:19 For the good that I want, I do not do, but I practice the very evil that I do not want.
Rom. 7:20 But if I am doing the very thing I do not want, I am no longer the one doing it, but sin which dwells in me.
Rom. 7:21 I find then the principle that evil is present in me, the one who wants to do good.
Rom. 7:22 For I joyfully concur with the law of God in the inner man,
Rom. 7:23 but I see a different law in the members of my body, waging war against the law of my mind and making me a prisoner of the law of sin which is in my members.
Rom. 7:24 Wretched man that I am! Who will set me free from the body of this death?
As Paul explains, the flesh (our body) is not eternal. Our spirit, which occupies a body, is eternal. Our spirit is the eternal part of our nature, and therefore it is our true identity. One day our body will die, and our spirit will live on to occupy a new body one day.
Therefore, God's curse on the ground impacted all that came from the ground, including plants, animals and the physical body of man and woman (who came from man). Only our bodies came from the ground since our spirit was "breathed" into us by God Himself (Genesis 2:7). God did not specifically pronounce a curse against Adam or Woman. Therefore, we know God did not curse them (i.e., their spirits), otherwise, they would have been condemned without hope of rescue.
Similarly, Christ’s physical body was cursed when He died on the cross taking upon Himself the curse God' pronounced on our flesh. Furthermore, His Spirit was separated from the Father for a time, taking upon Himself the punishment our sinful spirit deserves. Since He didn’t have sin of His own, He was not required to spend eternity in separation from the Father.
For a fuller explanation of Christ’s death, please read Why didn't Jesus have to stay in hell longer.