Is there a way to organize my library folder, so that songs are are catagorized: artist, album, song title? Right now, they are just listed numerically/alphabetically; eg 4 different artists all starting with song number 1, etc.

The basic answer is no. But you can click the bar at the top of any column to organise them that way. eg: if you hit the Size bar once, the smallest files will go to the top of the list, hit it twice & the largest will go to the top. MP3 Playlist has even less options however.