The Android "poltergeist" is most often a widget or app, and its associated services not playing nice with stock system services. The results can be as benign as fast battery drain or system slow downs, to as crazy as the things you describe.
A factory data reset resolves it, if in fact that is the issue. Backing up apps and widgets then importing them after the reset often reinstates the issues.. so it's best to really start over by installing from Play Store one at a time, testing for a day or so, then installing another app/widget. Very time consuming, but also very well worth it most often.