That’s what xmpp is. It was embraced by Google and Facebook and killed.

Lemmy is opensource, you can see and get a copy of the source code here. https://github.com/LemmyNet/lemmy There’s no development cost because all developers are volunteers at this stage.

For each instance that depends on the admins running that individual instance. The instance I use is being sponsored by a NZ company that are providing the admin’s a free virtual server to host on.