Goodlife, //what can you today learn from this case of Adam and Eve,//
Further confirmation that God wasn't omniscient. Poor choice on your part, Goodlife. Another story illustrating god's failings. Omniscience wasn't his strong point. Again from your bible.
//…and the man* and his wife went into hiding from the face of Jehovah God in between the trees of the garden. And Jehovah God kept calling to the man and saying to him: “Where are you?”//
Oops. Why search when, being omniscient, god really ought to have known where Adam and Eve were hiding?
As for Cain … poor old Cain. As a gardener all he had to offer God was the best of his crop, but since God prefers barbeque that fell far short of Abel's offering of meat. OK, Cain shouldn't have murdered his brother, I'll grant you that, but god made Cain human and therefore the responsibility is god's. Had god possessed rather more grace and rather better manners things might have turned out very differently. What an ungrateful god he was. Rude I'd call it!.
//In the case of Sodom and Gomorrah, Jehovah acted only after verifying the facts.//
Which were that in order to protect his guests from a salacious mob Lot offered his virgin daughters in their place and god judged him a righteous man.
What strange principles you have, Goodlife.