They are not out of date, this just show you the latest commit date/message related to the file/directory. You must NOT delete them!

This looks like either your or your friend probably made a mistake during commits with git. github (or any other git hosting services) never assumes any directory structure. If there's two copy of them, then one (or both) of you must have committed them. I would suggest to sync up with your friend before proceeding, and read up more stuff about proper git logistics.

They are not out of date, this just show you the latest commit date/message related to the file/directory.

After I switched from using WAV files to MP3 files all of my WAV files are still in the other directory, and they are not in the other.

Another strange issue is that only fetch works for me, not pull, and for my friend, vice versa.

Your local copy is probably messed up.

Every project should have a git url. Something like git@github.com:username/projectname.git.. Go to another folder, then do git clone git@github.com:username/projectname.git. git will create a new folder called projectname. If you go to that folder, you should see the same directory structure as the one you see on github.

Start cleaning up your project from this folder. You should read http://git-scm.com/documentation.