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I believe you pointed out at least one of your issues in your first line, Data Saver. Savers, of all types, data, memory, battery, usually have negative effects on the device they are installed on. This is true for antivirus and malware apps as well. You asked what apps the ability to change settings, these types of apps that we think are helping us because we often give these types of apps too much leeway and too many permissions. A lot of what some of these apps do is changing a setting to stop or prevent something, or for some other reason that is never quite clear. These types of apps also do things like try to scare you into getting other apps. Your data saver will start sending you ads for an antivirus apps. These ads can be deceptive and may look like a virus report, or a battery usage report saying you have too many apps running in the background, to get you to install their battery saver app. They are the Loki of Android, evil jokers that you cannot trust.
Do you have any other saver apps?
Do you have antivirus or malware apps installed?
My advice would be to disable all saver, antivirus, and malware apps on this device and see if your issues clear up.
If all of this started recently and you just cannot live a peaceful life without your saver apps, try force stopping and clearing the app cache and/or data for each of them. Clearing the data may mean you'll have to log in to the app again, and you might have to add some account information. For this reason I recommend cache first and data if it didn't correct the bug.
Let us know what you find.