Yes, the distinction between 'flesh' and 'Spirit' is made throughout the Tanakh.
Numbers 24:19 says that 'God is not a man'. We are told, instead, that God gives life to the soul. So God's Spirit is the breath of life. Spirit is life. Without this life, the body and soul are dead.
Not exactly true. God "formed man of dust from the ground, and breathed into his nostrils the breath of life; and man became a living soul" (Genesis 2:7). Man, the clay pot, is formed from dust, and it is the breath of God, breathed into the lungs, and therefore into the blood, in which the life exists. Upon death, the spirit of God returns to God. (Eccleciastes 12:7 The Soul is a compilation of the Spirit of God and the dust of the earth. When you die, your body will return to dust. The dust will not think, nor plan.
New American Standard Bible Eccleciastes 12:7
then the dust will return to the earth as it was, and the spirit will return to God who gave it.