Hmm, sorry i'm a bit inexperienced with playlists as I don't really use any media player for actually playing tracks! I just use them for ripping and burning. Maybe someone more experienced could help you? But I'll have a little go.....
I just tried to play WMA files on LW player and they don't play... As far as I know Limewire is just an MP3 player, but to use it you must first go to tools>options>player and then tick the box that says Use Limewire MP3 Player. I think you then need to restart your computer for this to take effect.
That should stop your system default player from overiding the limewire player and launching in other programmes such as Realplayer.
Try that if you haven't already done so.... also just to clarify, there IS a shuffle option, you just need to tick the box next to shuffle! Make sure your CD's are ripped as MP3 files. Then you just highlight the track you want to play and click the "to playlist" option.
Let me know how you get on.