I have to ask - why do you want to play mp3s in Media Player? It's crap in my opinion. You're much better off using the free app, Winamp on your PC. Although I HATE the strip-mall feel to the interface, it's better than WMP.
At any rate, I'm not sure what your problem is. Mp3 CDs created in iTunes work fine in WMP on my PC. What OS are you using on your PC? Using XP here.
About the iTunes icons. iTunes burns a run-of -the-mill Mp3 file. It's just that the file is associated with iTunes because it's the app that created it. If you were to use Audion, for example, it would have an Audion icon. The files you download have a QuickTime icon because your Mac doesn't recognize the creator but knows it's a multimedia file. QuickTime is Apple's default multimedia application.