Mac users can have files automatically added to the iTunes library...doesn't work that way for PC users
The shared "LimeWire Tunes" that you see in iTunes is just a playlist & so you won't be able to add those to a playlist or move them to your iPod...those aren't actually in the iTunes library. If you turn off LW's iTunes sharing, or close LW, that list will vanish.
You'll have to add files to the iTunes library first, then sync your iPod. Have a look at this thread (posts #7, #8, #9 in particular) for heaps of info & tips
Transferring music to iPod & iTunes