Did you get asked your password before? Not that you're confusing the password demand for your account or the Nintendo Network ID (NNID, which will pop up every single time you want to access to the eShop) with one for the Nintendo Online?
I was asked to link a Nintendo account, used my facebook that had saved the account and was able to log. Then it asked for a sub code with 4x4 code.
South American countries only have a limited version of the eShop available where you have to purchase codes on a separate website and then redeem them on your Switch. That's the 16-digit-code you get asked to enter.
It's possible for anyone to change the country on their console and access other versions of the eShop, so I assume that most South Americans use the USA version where all content can be browsed freely. You can try ask someone like mzuzek via PM how exactly it works, or alternatively use Google to search for quick guides on how to set things up. It's probably easiest to create a new account on the Switch console and use that one for purchases; the other accounts should be able to access all purchased content without problems.