Is it making an opponent's life easier if I explore their systems for them? Or do they have to explore separately to find the same thing? If there's a one-off event or bonus to receive does it go to the first person to explore or to each person differently?

Curiosity exploration is competitive. There is no second place for exploration. So, yes if you discover luxuries it will be visible to anyone. But there are still lots of reasons to explore others' curiosities.

• You can get small amount of discovered resources.
• Sometimes you can get rewards instead of resource deposits. Some of them (modules & improvements) are super powerful.
• Exploration grants decent amount of experience points. It's one of the easiest ways of raising your low-level heroes.
• If you happens to assimilate Pulsos and get industry-per-exploration assimilation trait, you should do anything you can to explore curiosities as many as possible.