Default Music app deleted from file system I have a jailbroken iPhone 5s on 8.1.2. (B440).

My son (for whatever reason/long story) has deleted the music icon/app from the home screen. He did this from the main filesystem thinking he could copy it to pc then put it back… he can't!

Further, I have tried to restore the phone using my back-up and by using my 8.1.2. ipsw but it wont work. I get errors saying e.g. firmware file is not compatible or cannot read library .itl as it was created by a newer version of iTunes. I've also tried restoring via basic recovery mode and DFU mode but get errors as above.
You won't be able to restore 8.x anymore because apple isn't signing off on that version. You'll need to restore to the latest 9.3.2. Yes you will lose your jailbreak and erase your phone by doing that, but the backup should put your settings back.

Keep in mind since your phone was jail broken and in a questionable state due to your son messing with it, there is some chance that you'll end up with a bricked phone.