- Grab APK from another of the SAME model phone running the EXACT SAME ROM your phone is:
The only thing you may be able to do is grab a settings.apk from another phone with the exact same ROM.
- Re-Flash just the System partition:
Otherwise you will need to re-flash your ROM. Don't Panic!! If you just format the following via the Recovery menu:
- ART/Dalvick cache
- and Cache
you can retain all your apps and everything else in /data.
Note: You may wish to do a backup of your launcher settings if you use something like Nova or ADW or Apex or Go custom home launchers (stock won't have a layout backup function). The only settings you may lose are any system settings (though MOST will be backed up anyways for you as most apps in /system use an area of /data to store settings files. Some do not and is why I mention it) that do not save their settings somewhere in /data or /sdcard.
Other than that, this process as such (as long as you do not delete /data) will retain all your apps and their settings (the boot after the flash will take longer than usual as it will need to generate the cache for all the extra apps on the initial boot, but an extra couple min is a small price to pay to not have to re-setup everything IMHO ;-) (and you should get a countdown as it is running through the apps)). AND since you will be flashing the exact same ROM there is no chance of problems [when changing ROMs if they use a different code base you can run in to issues where you are forced to format /Data as part of install, BUT NOT THE CASE when flashing the exact same ROM].
Tech Note on How This May Have Happened and Ways to try and defend against this sort of thing (nothing is a guarantee)
The only way something could mess with anything you have in the /system partition (including the system settings menu) can only be messed with by an app that has root access. So, be careful what apps you are granting SuperUser access to (and be VERY VERY VERY careful if you download apks outside the Google Play Store. It may seem like a good idea, but crackers can take ANY apk and add a virus to it and put it on a random site. Then you think you just got the newest angry birds and in fact you did, BUT they added a nasty surprise to it.
You could also try out a Virus scanner (ONLY download this via the Google Play Store, and ONLY use reputable big name brands to be safest. If unsure just fire up google and google the name of the anti virus and read up on user reviews and related material to get a feel for if what you are looking at is a good and safe option. Of course, even if you have a virus scanner something may still get by it so still best to keep things like the above paragraph in mind at all times.