iPod and the iTunes Library

Here is the question I need to answer: Do I need to keep my Libraries matched on each computer if I intend to update my new iPod (huge grin!) -- or sync it -- on multiple computers?

iTunes allows me to authorize up to five computers for use with one account. That's cool. iTunes also allows me to "deauthorize" a computer when I get the total up to six -- that is, deauthorize No. 5 and add a new No. 5 instead.

iTunes also allows me to copy downloaded music purchased from the Apple Music Store from one computer to another. This took a little time to figure out, but I got it done:

First, copy the entire folder(s) containing iTunes music to a data CD, USB drive, etc. On a Windows computer, they are way down deep, in Documents and Settings > [username] > My Documents > My Music > iTunes > iTunes Music (whew!).

INSIDE iTunes Music, you'll see the folders you want to copy.

When you put these folders onto a different computer, DO NOT put them inside the same iTunes Music folder. You can put them anywhere, but make sure it's OUTSIDE that folder on this (second) computer.

Then open the iTunes application and import the folders this way: File menu > Add Folder to Library.

So far I have done this only with music downloaded from the Apple Music Store. I don't know yet whether it works with other music files and folders, but it ought to.

So, back to my Library question: I have updated my iPod on one of my two authorized computers. When I tried to update it on the other computer, it would not work. Further investigations to come.