"iPhones are taking screenshots by themselves: [...]Are my devices hacked?: [...]My devices don’t always be in my hand when it happens. I’ve shown it to many people to prove that I’m not accidentally doing it myself."
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Hacked iPhone:
No one can hack an iPhone unless it has been jailbroken. And the only way to know if that has occurred is to know if it has been. So, if purchased form apple, then no worries there.
Restore to Factory Settings:
If you are so concerned, then restore your iPad to factory settings. Go here: What to do Before you Sell, Give Away, or Trade in your iPhone, iPad, or iPod touch - Apple Support
Backup Prior to the Reset:
IMPORTANT: Create a backup of your iPhone prior to performing all of this. That way, you can have something to restore if from, should anything go wrong with the restore..
Backing Up Items:
Note that all downloads would be lost. So, make a note of Apps that were downloaded. Also, enable items in iCloud, so that all is backed up. As an example, here is how to backup Contacts...
I. Enable Contacts in iCloud Settings:
Is Contacts enabled in iCloud Settings? If not, then enable it, and see if it pops up. If so, then it is gone amongst all devices associated to your Apple ID. So, to enable it:
A. Enabling on an iPhone:
Enable Contacts in iCloud:
- Go to: Settings
- Tap: your name (top item)
- Tap: iCloud
- Tap: Contacts (so that it is green)
and...
B. Enable on a Mac:
Is Contacts enabled in Apple ID on your Mac? If not, enable it.
- Go to: System Preferences
- Click: Apple ID
- Enable: Contacts