Adam also ate from the tree of knowledge. If they were equal before, why should she lose her equality and not Adam?
It's mathematics, boy! You can't argue with mathematics! [/Foghorn Leghorn impression]
It's pretty simple, really. When you take two things that are equal and make one of them unequal, the other one automatically becomes unequal too. If you make one of them less, you automatically make the other one greater.
What makes you think that God would have different punishments for male and female and why would he punish Eve more than Adam?
The text says plainly that He did. He said to the woman that she would be subservient and have pain in childbirth. He said to the man that he would have to sweat to earn his bread. He said to the snake that he'd have to crawl on the ground and people would hate him. It doesn't say that He punished Eve "more than" Adam, just differently.
Is punishment tied to gender?
There were three individual punishments. The pain of childbirth could only apply to the woman, of course, but otherwise they're based more on stereotypical gender roles than on gender
per se. A woman of today who chose career instead of marriage and children would be "choosing" Adam's punishment instead of Eve's.
If nobody died, where are A & E and what was the purpose of forbidding the eating of the tree of life?
Nobody died until much, much later - and of natural causes. If you say you're going to kill somebody and they die many years later of old age, that isn't murder.
They weren't forbidden to eat from the Tree of Life.
After they ate from the Tree of the Knowledge of Good and Evil, they were expelled from the garden to prevent them from eating from the Tree of Life. The explicit reason was so that they wouldn't live forever.
And no, preventing somebody from living forever is not murder.