You've got it mostly right. But this part is wrong:

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?

(assuming you're on desktop browser) If you want to browse only lemmy.world communities, click on "local" at the top:

"Subscribed" is all communities you specifically subscribed to (on any instance in the lemmyverse) and "All" is everything on lemmy.world AND all communities anyone on lemmy.world is subscribed to.

(fwiw, my account is on a different instance, startrek.website, but I subscribed to this community, so I saw your post in my "subscribed" feed).

So each instance within the fediverse can communicate with each other, but how do things like the feeds work? 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?

There is an algorithm and they're adjusting it to try and keep it interesting currently. It depends on whether the instance had contacted the other instance (through a search) or not as to whether they show up on the front page. Also, each instance owner says what to seed their front page with, that's why lemmy.world probably looks different than a niche instance. Someone just explained this to me.

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

It varies between lemmy vs mastodon vs kbin, etc. Each one reads and expresses their info differently.

Sorry, last one. I noticed there are things like music streaming and video sharing instances within the fediverse, so could Lemmy theoretically allow content from those instances to be cross-posted here?

Yes but I think there are people who have to develop it. Someone more knowledgeable has to answer this one.

Basically to me this feels like a super modular super media platform that has tons of parts that can plop in and out of the system as needed.

I think you're right but basically it's all in the beginning stages, volunteers coding it, and they're still putting out fires from the reddit migration. It will take a bit.

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.