Main question - Do we inherit the sin of Adam and Eve based on Romans 5:12?
Romans 5:12 New International Version - Therefore, just as sin entered the world through one man, and death through sin, and in this way death came to all people because all sinned
I will not repeat what has been said by agarza & Austin below, as they provide a good analysis regarding sin
The passage above at first reading implies: Adam sinned when he disobeyed God by eating from the forbidden tree, as a result all descendants of Adam inherit the sin of Adam, which means that all human beings are born with this original sin.
Paul further says:
“Therefore, as by the offense of one [Adam] all men were taken to condemnation; so also by the Justice of one [Jesus] many shall be made just.” (Romans 5:18–19)
“For since death came through a human being, the resurrection of the dead [on judgement day] has also come through a human being; for as all die in Adam, so all will be made alive in Christ.” (Corinthians, 5:21-22)
“And without shedding of blood there is no remission.” (Hebrews 9/22)
Summary; the above few passages imply that death came to all people due to inherit sin of Adam & Eve and that Jesus died for our sins with his blood
The above is the obvious reading of the passages at first glance.
However, should the statements be taken literal / non-literally / hyperbole / rhetorical
To answer this we would have to have a comprehensive analysis of all relevant passages.
“The son shall not bear the guilt of the father, nor the father bear the guilt of the son. The righteousness of the righteous shall be upon himself, and the wickedness of the wicked shall be upon himself.” [Ezekiel 18:20]
“Let the little children come to me, and do not forbid them, for of such is the kingdom of heaven” (Matthew 19:14). (We may well wonder how “for of such” could be “the kingdom of heaven” if the unbaptized are hell.)
“Let the little children come to Me, and do not forbid them; for of such is the kingdom of God. Assuredly, I say to you, whoever does not receive the kingdom of God as a little child will by no means enter it.” (Mark 10/14–15)
Deuteronomy 24:16 - 16 Parents are not to be put to death for their children, nor children put to death for their parents; each will die for their own sin.
“Then the Lord said to Cain, “Why are you angry? Why is your face downcast? If you do what is right, will you not be accepted? But if you do not do what is right, sin is crouching at your door; it desires to have you, but you must rule over it.” (Genesis 4:6-7)
Matthew 18:3 - 3 And he said: “Truly I tell you, unless you change and become like little children, you will never enter the kingdom of heaven.
Matthew 4/17, as we are told about Jesus: “From that time Jesus began to preach and to say, ‘Repent, for the kingdom of heaven is at hand.’”
Genesis 8:21 - 21 The LORD smelled the pleasing aroma and said in his heart: “Never again will I curse the ground because of humans, even though every inclination of the human heart is evil from childhood. And never again will I destroy all living creatures, as I have done.
Isaiah 7:15-16 - 15 Butter and honey shall he eat, that he may know to refuse the evil, and choose the good. 16 For before the child shall know to refuse the evil, and choose the good, the land that thou abhorrest shall be forsaken of both her kings.
Ecclesiastes 12:6-8 - 7 Then shall the dust return to the earth as it was: and the spirit shall return unto God who gave it.
Hebrews 12:9 9 Furthermore we have had fathers of our flesh which corrected us, and we gave them reverence: shall we not much rather be in subjection unto the Father of spirits, and live? (Spirit is not inherited by the parents & clearly babies are not born in sin)
Leviticus 5/11 - 11But if he cannot afford two turtledoves or two young pigeons, he may bring a tenth of an ephah of fine flour as a sin offering. He must not put olive oil or frankincense on it, because it is a sin offering.
Sub question - death came to all people because all sinned?
Ecclesiastes 9:2-4 - 2 Everyone will die someday. Death comes to godly and sinful people alike. It comes to good and bad people alike. It comes to “clean” and “unclean” people alike. Those who offer sacrifices and those who don’t offer them also die. A good person dies, and so does a sinner. Those who make promises die. So do those who are afraid to make them. 3 Here’s what is so bad about everything that happens on this earth. Death catches up with all of us. Also, the hearts of people are full of evil. They live in foolish pleasure. After that, they join those who have already died. 4 Anyone who is still living has hope. Even a live dog is better off than a dead lion!
Based on the above it is unlikely that Paul literally meant that we inherit sin, but was more hyperbolic language and how to earnestly follow Jesus as a saviour and avoid sin.
Otherwise, R 5:12 would be contradicting much of the other passages and could even be read as – implying that Jesus was born with sin, which clearly cannot be right.