Most actions federate, any exceptions which aren't federated yet are generally just there because the federation logic has not been implemented (but improvements are constantly being worked on).

Generally federating the modlog is mostly just there for informative purposes. As in, we can check what mod actions were taken on instance A through the modlog on instance B (and there is no mechanism in Lemmy for other instances to retroactively remove or hide federated modlog items, btw).

It federates...ish.

Some instances federate actions better than others, and even then it can be random which get properly federated- a lot of time site/community bans don't get federated to the modlog right but content removals almost always do. I have a feeling this is largely intentional.

The most reliable method is always to check the home instance of the community/user directly.

It is, but the only fully federated things are instance oriented moderations. No one can federate out changes on to communities on other instances. Those actions would only show for their local users.

Not everything federates. Not everything needs to. For example, if you ban a user from a local community, that action is handled locally.

I think. I'm not completely clear on which data is stored on your instance and which is on the remote instance.

For which community?