Well… Eve still would have sinned, wouldn’t she have? Wouldn’t that mean that the original sin of our first mother would have been propagated to us?
No… this would imply that sin would not have been in the world. Even if Adam hadn’t sinned at that time, it doesn’t mean that he never would have sinned.
I recall vaguely that some saint or doctor of the Church said (but cannot recall who said it) that, even without the sin of our first parents, Christ would still have become incarnate and saved us.
No… even if that event hadn’t been sinful in the way it was, then that doesn’t mean that there wouldn’t ever be sin. And, therefore, there still would have been the Incarnation and the Virgin Mary, although the description of the first sin might have been different in its particular details.
No… with sin in the world – regardless of the details of the first sin itself – punishment for sin would still exist.
Now this is the interesting question!
In the time and place of the original audience of the first chapters of Genesis, gender equality simply didn’t exist. So, if Eve sinned but Adam did not, then there would not have been the recognition of the sin in the way that there was, given that he did. (It’s somewhat analogous to the question of guilt when a toddler harms someone – there is injury, but not the notion that the toddler is himself guilty.) However, one would have to ask whether Adam were guilty of failing to live up to his obligation to protect Eve – would that not imply a guilt of sin, as it were?
In any case, the Church teaches that Genesis 3 is a figurative narrative. That means that it isn’t literal historical truth, but rather, it tells us that our first parents did sin, and thereby they set in motion of chain of events that led to not only human death, but human salvation through Christ.
So, the answer to your questions, in a certain sense, is “don’t get caught up in the details of the story – don’t miss the forest for the trees, and don’t ask ‘what if that tree weren’t right there?’”…!