You can have a look at https://join-lemmy.org/docs/users/04-moderation.html to see a table with the different actions and the role required, as well as some explanation of how it works.

Personally, I received reports as a non-admin mod for a community from users from other instances, so that should be possible

If this is true, what is the admin of the reporting user even supposed to do

Decide what instances to defederate. They can check up on:

• Mods of other instances to see if they take appropriate action on reports.
• Admins of other instances to see if they take action against bad-faith mods.
• Admins of other instances who generate a disproportionate number of reports per capita, to address structural, cultural, or policy issues that lead the offending instance to be a bigger source of pain/reports than others.

And finally they can defederate if they don't like what they find.

I have 0 experience with the admin side of Lemmy, so I don't know what actions an Admin can take over a user from another instance. If I had to guess:

• In the post I linked before there is a comment talking about a "purge feature", but I don't know how that works.
• Community Mods may be able (?) to ban the user in that specific community
• Instance Admins may be able (?) to ban / block the replication of that user content in their instance

But again, not an expert, so I don't really know what is the intended way to handle this.