Do all people inherit Adam's sin nature?
Yes. When Adam sinned, he plunged the whole human race into that fallen condition, and all his offspring inherit the sin nature. Paul describes himself as carnal, a son of Adam, sold under the old Adamic nature or under sin. Thus every person is born into Adam's fallen line.
Les explains from Paul's words that the law is spiritual, but Paul calls himself carnal, a son of Adam, sold under the old Adamic nature or under sin. When Adam fell and sinned, he plunged the whole human race into that condition, so Christ had to die to bring fallen mankind back to Himself. Les notes that people may ask how God could call them sinners for what Adam did 6,000 years ago. He says he cannot answer that, but God's mind is higher than our minds and His thoughts higher than our thoughts. God sovereignly set it in motion: He placed Adam and Eve in the garden with one simple responsibility not to eat of that one tree, a means of testing their obedience, not because the fruit was wicked. Adam flunked totally and ate, and the sovereign God declared that now that Adam had sinned, all his offspring would inherit that sin nature.