Sounds like you've done everything correctly. As soon as an mp3 has downloaded, iTunes will open (if it's not already open) & copy (if you're fast enough, you can actually see iTunes go thru the process of copying the LW files to it's library the moment they've dwnlded from LW) the file to its own library which, depending on your user setup, should be found in your Users/(your name)/Documents/iTunes. That'll mean you'll end up with 2 copies of the mp3 (the other in your LW dwnlds folder.) A copy of all your LW mp3's 'should' end up in iTunes library.
"On another desktop the folder in iTunes hasn't appeared."
I am totally confused as to what you mean here!
You can add items from folders/folders of mp3's from anywhere on your mac (so long as you have permissions) by using the Adding to Library (CMD+O) option within iTunes. Can also change its Library location with Prefs. But don't copy all your existing iTunes files there unless you want it to if it asks you.