Reports federate, in a limited way. They federate to the instance the community is hosted on, the instance the reported user is hosted on, the instance the reporting user is hosted on (well technically, it doesn’t federate to the last one, as that is where it started). I don’t believe that a report will federate to a remote instance that doesn’t meet one of those criteria, even if it hosts a moderator for the community, but I’m not certain about this one.

Either way, report resolutions don’t directly federate, so resolving a report doesn’t resolve it on the other instances. It looks like they federate, because post removal from a mod federates, and removing a post auto closes the report. However, a report that was spurious or a troll or whatever that isn’t going to be actioned, has to be manually closed down on each instance it federates to.