how do things like the feeds work?

So what actually happens under the hood is when one instance communicates first time with another instance it builds some local cache of that remote instance. Then, when you open "All", you get everything from your local instance + things cached/requested from other instances. Admins can defederate an instance, in which case you would not see anything from it.

Since there's no algorithm is everything from Lemmy.world only going to show up on the popular feed (if I'm on that instance) or can other things like lemmy.ee or whatever also show up?

Everything federated will show up.

And can I comment on posts from a different instance or does that vary per instance?

If federated, you can both see and post both posts and comments on any instance from your home one.

could Lemmy theoretically allow content from those instances to be cross-posted here?

It could. More than that, Mastodon users currently can both subscribe to Lemmy instances and post/comment. It looks kinda weird since they mention post author/community or whomever they answer to in a comment, since they see it as if it looked like Twitter.