OK, so the home screen does come up, where you can see the list of collections (Hymns, Children's Songbook, Additional Songs for Children, Youth Theme Music)? It sounds like the app is opening. Is it a certain section of the app that's not opening for you?
LDS Music for iOS does currently support iOS 9, so it should work on your device.
Samuel Bradshaw • If you desire to serve God, you are called to the work.