1. wmp is a playlist player. It doesn't have its own library. So, wherever the songs are when you add them to wmp is where your song files are. I'd recommend moving your music to your Music folder before adding them to wmp. Unless you just want to burn them. Otherwise if you move or delete any of the songs after adding to wmp, wmp won't be able to play them b/c it won't know where they are.

2. To change default for files see Setting default audio program & this will change their icons.

3. Why you can't play some songs with wmp but can with mplayer2? Not sure. It does sound like a codec issue unless you made the mistake of no. #1 above. Have you updated your codecs. Are they really mp3 files or mp4 or m4a or ogg vorbis or something?