So once an instance is federated by another, those posts also live in the 2nd instance as sort of a backup?
When you are browsing a federated community from your home instance, you are essentially interacting with your home instance's copy of that community, which will be sync'd to the instance of the federated community.
Think of it like email essentially: If someone sends you an email, but deletes their own email account, you will still have that message history, but you won't get more emails from that account.
it sort of just feels like a chat room or something.
Lemmy is not Discord, the messages are persistent and structured in nested threads just like reddit or traditional forums, so they will be organized and searchable.
Besides, any website, including reddit, can go away at any moment, but that doesn't mean they will.
Do most people browse within their “local” or “all?
You can do both, or, you can just subscribe to communities that you felt are interesting.
"All" is useful in that even if your home instance has relatively low activity, you can still comfortably browse content everywhere across Lemmy/Kbin.
But if I have to search 15 other “news” to see discussion on something I am interested in, isn't that kind of cumbersome?
You don't have to look at all of them, just the ones you find interesting.