1. Ignore the LW playlist within iTunes. It doesn't mean much. You can play songs from that playlist but can't copy them.

2. To copy songs to iPod, you have 2 options. One is to auto-update the iPod with your playlist. The 2nd, which I'd highly recommend is to manually update (copy to) it. See How to transfer music to my iPod (& iTunes) There's links there about how to use iPod. See the entire 1st page!

3. Make sure the songs you want to copy across work ok. Test them to be sure that you haven't ended up with a dud mp3 file filled with silence or something.