Glitchy iPad - ghost in the machine?!

Hi there, I’m having some issues with my iPad. It has randomly started glitching as if someone else is tapping apps. When I try to enter text or numbers the ghost in the machine takes over and enters uuuuummmmiihhhhh or whatever - big string of rubbish. I’ve tried resetting - sometimes works for an hour or so. Last night I restored it back to as if it was brand new device - totally wiped it. Now it’s doing it again: enlarging items on screen when watching a movie, switching between apps by itself, typing rubbish. Any ideas what could be wrong and how to fix it? As far as I know it has not been dropped or anything. It’s in a protective case.

Thanks