Native Camera app deleted on iPad mini
It sounds like Camera is disabled in Settings > General > Restrictions. This removes the Camera and FaceTime apps. A similar post on Apple's forums said that the Photo Booth app was removed by this restriction.

This third-party article on an MDM tool says that the restriction removes the Photo Booth app:


  
  Disable Camera
  
  
  The camera will be completely disabled. This also remove the Camera, Photobooth, and Facetime apps on the home screen.
  
  


It would make sense that the restriction available in the UI flips the same bit as the MDM restriction.