Sorry if I get a bit technical but I'll try to explain my understanding.
Lemmy.nz has it's own communities. When someone subscribes to a community on another instance (say, !asklemmy) , the posts and community details are copied to a local version on the server. When someone from Lemmy.nz posts to the community, it goes into our local version. The server then behind the scenes is trying to keep our version in sync with the "real" one on lemmy.ml. Lemmy.ml is sending new posts and comments to lemmy.nz, and lemmy.nz is sending posts made by lemmy.nz members back to lemmy.ml, who then send them out to other servers.
If lemmy.ml suddenly disappeared, we would continue to be able to post to the community, add comments, etc, but sending those posts to other servers wouldn't work. lemmy.ml is responsible for sending the posts to your server at lemmy.world, and so you would not see the posts made by lemmy.nz users that are no longer able to federate - however, you could still read the community as it was at the time federation stopped and with the addition of anything anyone on your own instance has added.
One exception is media. Lemmy currently does not federate media, so if someone posts a picture to a community on lemmy.ml (where the picture is uploaded to lemmy.ml), then lemmy.ml goes offline, no one will be able to see the picture (but they will still see the post).
In terms of accounts, you will lose your account. However, accounts are also federated as remote users, so when a lemmy.world user like yourself posts to lemmy.nz, your account is also copied here. Lemmy.nz users can view the account, see that you made the comment, etc. However, you cannot log in to your account and make new posts from a different server - it's a sort of ghost account.
So long story short, you lose access to your account and any images but the posts and comments are accessible from other servers so long as they were federated with your instance prior to it shutting down. If a new instance comes online, it will not be able to get posts from a community on an instance that is no longer online.