Tina no idea
Lurker
Need settings.
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It looks like that one stopped with Kit Kat (Android 4.3) So I'll assume you never went beyond that. What I think has happened is that settings app was updated and it broke the home screen shortcut. I've seen a few apps do this, but it's nothing to worry about.
If you can open your app drawer, you should be able to get to settings that way. Then you simply have to long press on the settings icon in the app drawer and then drop it back on your home screen.
Please explain exactly what you are doing when trying to get to your "apk" files. These are not your apps, but the installation archives you use to install the apps.