You can use Windows Media Player by going to Settings/USB mode and switching to MTP, but watch out for WMP’s default setting, Auto-Sync, that tries to sync every file on your computer onto the poor little Fuze. Go into Tools/Settings and change the defaults.
Your computer can only see one USB mode at a time, MTP or MSC. It sounds like you transferred files already in MSC. If you switch to MTP mode to use Windows Media Player, the files transferred in MSC won’t be visible on your computer until you switch back to MSC mode (and then you can’t see the MTP files). The Fuze itself sees all.
You can use Winamp by going to Settings/USB Mode and choosing MSC.
You can use Media Monkey in MSC.
To understand how information is displayed on the Fuze, welcome to the wonderful world of ID3 tags. You can use mp3tag, the program described in the FAQ, to tag .ogg files as well as mp3.
If you want to go by filename, update the Fuze firmware to the latest version (see how in the sticky notes near the top of the forum) and you will have a choice of Folders under Music, along with the Artist, Album, etc. lists that it is getting from the ID3 tags.
Multiple albums from the same artist should show up under Artist as a list of albums–if the ID3 tags are correct.