how do i tell if apple remote desktop has been installed on my ipad without my knowlege

I would like to believe that there is no remote application for the iPad but contrary to what you say my iPad does its own thing when I am at home doing things like shutting off without pushing any buttons and then won't even start back up until it wants to as well as not being able to sign into iMessage or back up to iCloud. When I leave my house and connect to a different wifi it acts completely different