They all use the same protocol, but developers pick and choose features and how they are presented. They may be able to talk to each other but the experience also may not be ideal, especially if they use different features in different ways. For example, until a few days ago kbin upvotes didn’t show up in Lemmy at all, and Lemmy upvotes did not show as upvotes in kbin, because they used different features to describe them (kbin used boosts, which exist in Mastodon but are not implemented in Lemmy).

That's what I think happens but I'd like to know too

Your account credentials are the keys to your house, you can only enter to your own house (server/instance) with your keys, but can watch through everyone's window (the owner of your house can block some specific windows tho).

So your second assessment is correct, and yeah I think if the server goes down your data in that instance may be lost. It shouldn't pass long time before some migration account feature (mastodon already has one).

I don't think Lemmy has good support for viewing Mastodon content (unlike kbin), but you can view/follow users, threads and comments from Lemmy on Mastodon by searching @whateveryouwant@instance

You do everything from your home server.

So you're at feddit.it, instead of going to https:/lemmy.world/c/lemmy.world you go to https://feddit.it/c/lemmy.world@lemmy.world

I don't know how posting between mastodon and lemmy works.

And yes, if your instance dies, your account is gone. Mastodon has a "transfer account to another instance" feature, but Lemmy does not yet, but I'm pretty sure redundancy in some form is planned.