1. The "status bar lock" may not work on some phones because it is an undocumented Android feature. For example, it may not work on Android 9 and above.
To disable exit to settings, please make sure "android.app.settings" app is not present in the configuration, and you have granted the "access to app history" permission on the device.
If you still want to lock the status bar, consider using "Kiosk mode", it effectively locks the status bar and navigation bar on Android 7 and above.
2. Unfortunately the mobile data couldn't be changed programmatically, even by a MDM admin app. So the only way is to force user to change this setting in the UI.