If Eve is the mother of all living, was she the mother of Adam? was Adam the Father of Eve?
It's a myth.
Was Eve the mother of all the men and women in Nod?
Genesis:
15 And the Lord said unto him, Therefore whosoever slayeth Cain, vengeance shall be taken on him sevenfold. And the Lord set a mark upon Cain, lest any finding him should kill him.
16 And Cain went out from the presence of the Lord, and dwelt in the land of Nod, on the east of Eden.
17 And Cain knew his wife; and she conceived, and bare Enoch: and he builded a city, and called the name of the city, after the name of his son, Enoch.
Christ revealed a whole different view of the Eden myth. The catholics rejected it to creatae an orthodox view since it disputed Moses.
John 6:32
Then Jesus said unto them, Verily, verily, I say unto you, Moses gave you not that bread from heaven; but my Father giveth you the true bread from heaven.
Only the Spirit (capital S) reveals the truth. Man didn't have it until Christ (not Jesus) gave it. John 20:22
Many scriptures were written due to this Spirit. Most rejected to see the OT instead, by people who never had it.
At least that is my view from a lifetime of seeking in all places, and not just the church.