Simply put, yes. In the same way subdomains are independent of eachother (for example balls.microsoft.com vs balls.apple.com), communities in different instances are independent of each other, even if they share the same name. That's because a communitys full designation is, for example !asklemmy@lemmy.world
As for the multiple mod accounts on different instances, this is often because the mod-log and reports often don't federate properly, so it is common for mods to sign up an identical account on the instance of a community they moderate.
When it comes to creating identical communities, first thing you need to ask yourself if you should. Sure, if an identical community exists on a different instance, but it's dead, it shouldn't be a problem.
However, when there's already an active community, it's better to join and contribute to that one, as fragmentation isn't really helping anyone in particular or the fediverse in general.