A very simple way to check which desktop manager you're using is to right-click on the panel. For Kde you'll see "Help" => "About KDE". Gnome just has "About Panel". This will give you version info, etc. for either kde and gnome as well.
MP3 support doesn't come with SuSE out of the box. If I remember correctly, SuSE stopped shipping with MP3 support since 9.3. Because MP3 is a propriety technology they stopped shipping it for legal reasons. They did the same for DVD playback. Pop an encrypted disc into the drive and you'll get an error message to the effect that DVD playback isn't supported. You didn't mention anything about that so I won't elaborate on that here. Just ask, though, if you need help.
I personally use the mplayer essential codec play. It provides a wide range of audio and visual codecs - I haven't yet encountered a file that I couldn't play back thanks to this pack. You can download it from http://www.mplayerhq.hu
. It comes as a tarred bzip package. Open a terminal and untar it with:
# tar jxf essential-<package_date>.tar.bz2 (If you press tab after typing the first few letters of the filename it will autocomplete it for you)
Then copy the contents of the directory it creates (you'll need to be root)
Enter root password:
# cp essential-<package_date>/* /usr/local/lib/codecs
If /usr/local/lib/codecs doesn't exist you may have to create it first:
# mkdir /usr/local/lib/codecs
And that's it! You should now be set to play mp3's in any app you choose.