If there was no correlation between gender and your behavior (e.g. perhaps due to non-existent gender roles and expectations), do you think the world would be a better place? This does not mean that everyone on earth becomes a hive-mind, but rather, as I said in the start, that gender plays zero role in your behavior. Just like how the length of your name or the color of your hair plays no role on your behavior. You probably can't tell apart the behavior of people with 4-letter names and people with 6-letter names (nor would you expect them to have any differneces in behavior) - so imagine if this was the case but with gender. Zero gender roles; zero gender expectations.

Either men become more like women (and women stay the same) or women become more like men (and men stay the same). Or they both meet someplace in the middle. Up to you for the premise of this question. Be creative

Here's my take: yes the world would be a much better place. Most of our gender problems come from the fact that men and women behave differently, due to a number of biological and societal factors. For instance, if men sought out relationships and sex at the same rate that women do, everyone would benefit.