Multiple malfunctions on my iPad mini

My iPad mini has taken on a life of its own. Apps open and close on their own, components of games either move on their own or lock and won't move at all, (i.e. jigsaw puzzle pieces in Magic Puzzle app spin and move in and out of puzzle area without any touch to the screen). The device is nearly unusable. It has 56.6 GB of memory and 19.8 available. The system is current; no updates are available. How do I fix this?