My MacBook will not download any apps. What can I do?

What happens when you try to download an app? Error message(s)?

Have you tried restarting the computer? Are you running any anti - virus programs? Using a VPN?

Try setting up another admin user account to see if the same problem continues. The intent is to see if it is specific to one account or a system wide problem. This account can be deleted later. 

Isolating an issue by using another user account 

If the problem is still there, try booting into the Safe Mode using your normal account.  Disconnect all peripherals except those needed for the test. Shut down the computer and then power it back up after waiting 10 seconds. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. When you reboot normally, the initial reboot may be slower than normal. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application un-installer or by using the developer’s uninstall instructions. For each disable/delete, you will need to restart if you don't do them all at once. 

Safe Mode - About.    

You should be able to download apps as long as they are compatible with Sierra.

Are you running any anti - virus programs? Using a VPN? Did you try another admin account and the Safe Mode?

Not yet. In my original post, the two light blue items are links that explain how to test in another account and how to boot into the Safe Mode.

Did you try testing in another user account and the Safe Mode on your computer?