After you register, we need to know more. What's happening when you tap an .apk file from a file manager? (.apk files are app installers, they're not apps. When you "run" an .apk file, what runs is the installer, and it installs the app.)
If you're downloading .apk files, they may not be for your phone, or for your version of Android. Only use Play to install apps - then you get the correct version and, if there is none for your phone, you won't even see the app.