Ghost/phantom notifications and other sketchy things my girlfriend's phone started doing something strange recently – after Airdropping three photos from a slightly older iPad Air, the notification center has been acting strangely. Every time she opens it, an animation plays that looks like the back end of the animation of clearing all notifications – just a couple empty bubbles disappear upward. She did a hard reset, and noticed a white horizontal line on the screen appearing during the reset, which is also new. 

The iPad is also acting up now, which is new. When I go to the Photos app and try to open the camera roll, it opens, scrolls automatically up to the top, then closes and goes back to the grid of albums. This happens both with an internet connection and without, and has never happened before. It also switched to the Find My iPad app on its own, which is a little freaky.

The iPad is not password-protected and hasn't been for a couple years, but the battery has been dead for at least a year – she only charged it back up yesterday and started using it today. We're concerned about malware somehow getting onto the iPad, and then from the iPad to the phone. Our wifi network is WPA2 password-protected, and as far as we know, neither of us has downloaded anything sketchy onto the phone or the iPad (or anything else). These issues haven't been happening on any of my Apple devices. Is there a chance something might have somehow gotten in? How do we fix it? Even if it's not dangerous, the notification thing is pretty annoying and I'd like to fix it for her.

Thanks in advance for the help. I used to be really good at spyware removal and such up until a few years ago, but my knowledge has atrophied since then and I'm pretty much useless now.
This sounds like a failure of the digitizer. All sorts of phantom scrolls and clicks can happen when the hardware thinks it's detecting fingers making tap and scroll motions at random or repetitively.

If you open the calculator app, sometimes you can map out what parts of the screen are failing, but depending on the severity it may come and go in relation to percent of charge and temperature.

Long term, this is likely to get worse and need a repair - especially if the phone has been dropped and suffered either internal damage (which can be 100% invisible - especially if you have a case protecting) or can be totally unrelated to any damage - just that the fine wires in the display have stopped working as designed.