Yes and yes.
Your user "exists" on the instance you registered on. Think of it as creating a user on gmail, and a user on yahoo mail. Two separate users tied to each mail service. If yahoo mail were to shut down, all your messages in yahoo mail would be gone. Any messages you sent to gmail would still exist in gmail though. So, any posts or comments you had made outside your instance (on other instances) would still exist. You just wouldn't be able to log in as that user anymore.
If the account user name you want is taken on lemmy.ml, you can sign up on lemmy.world or beehaw.org or some other instance, then browse from there. Keep in mind, that even if your "account profile" name is taken, you can still set your display name in settings to what you wanted.