I see alot of people using an email analogy that people don't seem to follow, I saw another analogy so I'll give it a go (and probably butcher it haha.)

You have the planet, right? "Lemmy" as a concept, the "Fediverse" is the planet. Then, you have countries. Large, all encompassing central entities, each with it's own ruling government and systems. What you can get away with in Ireland, might not be legal in Turkey. Instances (or servers) like lemmy.world, lemmy.ml, etc are the "countries." Each can have it's own standards, practices, rules, etc. Then the communities are like cities in those countries, beholden to the larger entity but otherwise allowed to run themselves and do what they do.

For your last question, let's look at those communities (cities, per our analogy.) Say I live in Franklin, Maine. Around town, if you're talking about home you don't say Franklin, Maine all the time do you? It's just Franklin, because if you're in Maine (or your home country if not US) it's presumed you're talking about the Franklin that you're in (or the Franklin down the road if you live two cities over.)

There's still a Franklin in Alabama, Idaho, Illinois, Michigan, and like 40 other states. ^(Thanks wiki :P) So if I wanted to talk about or visit one of THOSE Franklins, I would specify Franklin, Idaho, or Franklin, Illinois. That's the "Fediverse."

(Pretend for a minute we are in a community /c/puppies for this bit so it's less confusing) This group, for us, is just /c/puppies because it's our local /c/puppies, just as I from your perspective am just @CannaVet because we are both in our home "country" of lemmy.world (the instance/server.) If you look at one of the replies to the comment you replied to, you will see someone as @JakeBacon@lemm.ee. He is visiting our "country" of lemmy.world, from his home "country" of lemm.ee. Over in the "country" of lemm.ee, they may also have a community (city) of /c/puppies which is notated as such to HIM because it's local to his home country just as ours is to us - but for us to visit would be "traveling" so we would visit /c/puppies@lemm.ee because we're leaving home and visiting another country. For him to come here he has to come to /c/puppies@lemmy.world because HE would be the "traveler."

Same with users, I'm just @CannaVet and you're just @Swoggles because we're "at home" on lemmy.world, but if we click around and are perusing a community on lemmy.ml we would show as @CannaVet@lemmy.world and @Swoggles@lemmy.world because we're "traveling." There may be a @Cannavet@lemmy.ml, but on lemmy.ml they would just be @CannaVet and I would be @CannaVet@lemmy.world, because I'm visiting their "country." If they come here I'm @CannaVet and they're @CannaVet@lemmy.ml.

We're different users, with different accounts, on different servers, completely unrelated. Communities work the same way - I may run /c/stuff@lemmy.world however I want, but somebody might be running /c/stuff@lemmy.ml completely differently with completely different rules and content entirely over on that instance.

As for exploring different instances, you can go most anywhere you want (mostly, my understanding is instances can block other instances from access, but I'm not super in the know about that.) Using the "all" button in search and browsing will open you up to other instance's content vs the "local" button that keeps you in your "home country."

I don't understand entirely how to link out to other instances, but if you click a link and end up logged out on a different server, you can manually visit by adding the community to the end of your URL like so-

lemmy.world/c/technology@lemmy.ml

This will keep you on lemmy.world and ensure you're "just visiting" where you're trying to go. Once everyone has a better grasp this shouldn't be a problem but I've run into this issue a few times.

Cliffs Notes-

Instances (lemmy.ml, lemmy.ml, lemm.ee, etc) are top level "countries" and run things as they see fit

Communities (/c/puppies, /c/lemmy.world, etc) are "cities" bound by instance administration and can exist on multiple instances completely independently of eachother, like how London, England exists independently of London, France.

If you run into trouble visiting communities on other instances, manually navigate with lemmy.world/c/commname@instance.url (or lemmy.ml/c/commname.url if you're registered on lemmy.ml, etc etc.)

Sorry for the wall, hope it's at all helpful lol.