My development/testbed instance is hosted on its own Hetzner server via a separate subdomain of my existing domain. It does need to be exposed to the internet to test federation, and it does need a domain to my current understanding (in that I haven't tried it with just an IP address). Email is a very good analogy, as the original well-known federated web communication tool. :)

There is a way to install and run kbin via docker, that's what I use for both my dev and prod setups.

I would highly recommend familiarizing yourself with the ActivityPub spec to understand what you're looking at, and try GETting a few comments, threads etc via Postman. ActivityPub, much like email, is peer to peer, account to account. An activity comes from one actor to another. So understanding kbin necessitates understanding things like "a magazine is also an actor" and "the reason threads and microblogs are different is because they have different activity types."

Once you've got a handle on that, the psql database will make a lot more sense when you explore it, and you can connect all the dots together. Even though I do not have more than a rudimentary grasp on PHP, with the current understanding of ActivityPub and the database I have I'm slowly putting all the pieces together. :)