If you use the Assistive Touch feature, you might have set up Custom Actions that allow you to take screenshots by tapping the Assitive Touch menu button. (might not be available on your version of iOS).
Some keyboards might have a screenshot key. I’ve never seen one, but who knows.
Screenshots don’t happen without some indication (a click and quick animation on pre iOS 11), so I’m not sure how you’d miss noticing you were doing it.
For a third party app to save pictures to Photos without you noticing, it would need permissions to save to the Photos app. Check out your privacy settings and see what apps have access to Photos. That may offer a clue.
I can’t remembe where the privacy setting were on iOS 9, so you’ll have to hunt around. Unless someone else with an older iPad offeres directions.