the media player will play whole songs, but i don't think it has any support for playlists at all. i.e. you pick a song and listen to it. then you pick another song and listen to it. i don't know for sure, but i doubt that there is "true stereo output" the phone is not designed at all to be a mp3 player. it really just has basic functionality.
if you want an mp3 player, go with the slider remix. if you want a super skinny motorola, go with the razr!