Perhaps I am not totally understanding you
You mention iPod Library. ... There is no such thing. There is iTunes Library and Limewire Library.
The green music icon, I am assuming is a semiquaver (or something ... a long time since I scraped thrugh grade 2 piano lol) with mp3 written under it. This will have a .mp3 extention.
The files you are mentioning. Do they have an extention ? If so what is it? If the extention is m3u then these are not music files they are playlist files which appear in Windows, but not in mac (which I use) afaik .
Please tell me where you are seeing this icon. and also go to limewire options or preferences > saving > save folder. go to this folder and see what the files there look like. and do they have an extention.
Also: Is this the first time you have installed iTunes, and what was your mp3 player on your computer before you got iTunes?