true indeed Adam was the one God told not to eat from the tree, IMO I think Adam told Eve as well about that tree, then again as you have stated it's not mentioned, so God could have said this to Eve later on as well, but reading and knowing how God's ways are, not all the time God comes to every person, If this was so there wouldn't be any need for prophet's etc.
God will use a person for a message delivery and then it's up to the people to believe it's from God, many times in the OT people did not believe in the prophet's words even though they knew they were a prophet, I fine it interesting how someone can say this man is a prophet yet don't believe the words they say. The deciples were kind of like that a little bit sort of, they believed Jesus was the Son of God yet struggled with believing every word He said, over and over He explained the resurrection and shown examples of it yet after it happened they didn't understand what had happen it took awhile for it to dawn on them, what does Thomas say "I won't believe it until I place my fingers in the hole of His side". That Old saying you can lead a horse to water but you can't make the horse drink.
Eve was the one who got deceived by the serpent for the serpent spoke of a truth and lie at the same time, this is why the serpent was punished as well for that action that happened at the tree of knowledge of good and evil, the serpent did just that, So three were punished, the man, the woman, the serpent.
Some people think evil can't speak of truth that is of a misunderstanding, example of this is when Jesus came around a demon, the demon would use words like " Jesus the Son of God" I'm one who believes this is a truth.