Where can I find a music editing software that lets me insert and edit clips of music? Free, maybe?

well i dont know if they will help but you could try
audio trimmer
online audio trimmer

Why not try Joyoshare Video Joiner? Although it is not a totally free one, you can use it to edit clips for free if you use it no more than 5 times. With Joyoshare Video Joiner, you can cut the unwanted sections of videos or audios, and then merge the rest without quality loss. It is a really nice video editor.