Chosen Solution
The iPad is living its own life, it opens apps and pages by itself. It looks just like somebody else is remotely using the iPad. This fault happens intermittently, when it happens and the iPad is re-started it usually goes away for a while. Is there a common thing on the iPad that causes this behaviour? A restore does not seem to fix the problem.
It sounds like the digitizer is suffering from Ghost Touch. In those circumstances, the iPad will register touch commands that weren’t given by the user. This could be caused by drops or impacts, either a major one or multiple small impacts over time. It could also be caused by a previous repair (low quality digitizer or faulty best practices). In order to fix this, you could order a good quality digitizer (this is essential) from iFixit and follow the repair guide here.
