Every server is under the total control of it’s admin while moderators are self-assigned to communities by the users that created them. It’s literally the exact same structure as on reddit.
The only difference is that there only is a single reddit server with a single set of admins, while lemmy has many instances.
So yes, everything you mentioned is basically the same on both platforms. The only difference on lemmy being that when you piss off the admins and get banned you can go to another instance.
Someone call Van Halen!