Why is it when I download music, I can only playback when I'm connected to a wi-fi conncection?
Are you sure you are not using a cloud storage service (Google Music for example) and not actually downloading the music? Though not sure why you wouldn't be able to access it on mobile data.
If it was Google Music, I know there is a setting that restricts playback of cloud stored music if the user choose to set it that way.
That makes sense, I never use streaming music or cloud music storage because it's too hard on my battery, so I wasn't sure.