First of all what are you files downloading as?
Go to file\get info\general information. this will tell you what they have been downloaded as. If it says that it is a limewire document you will need to download again as these just return to limewire. If the problems persists it best to delete and re-install limewire.
To get mp3's to open in itunes make it the default internet player by opening itunes then go to edit\preferences and in the general tab press the button "use itunes for internet playback"
Hope this helps.