Apps open then immediately close. App Store empty. Unable to install new apps.

I downloaded various Mac cleaning and antivirus file

Well I suspect this is half the problem, your macOS has been compromised.

From a safe boot, you maybe able to download and run the small utility http://etrecheck.com to get a good look at your system config. for conflicts or issues.

Try a SafeBoot  https://support.apple.com/en-us/HT201262

Takes noticeable longer to get to the login screen, does a 5 minute disk repair before it fully boots up, and certain system caches, dynamic loader cache, etc. get cleared and rebuilt.

If no luck Boot into Recovery (Command R) and from the dropdown menu: Utilities>  Disk Utility> run the First Aid on your Macintosh HD. If errors are found and repaired, run again until no errors reported.


Recovery http://support.apple.com/kb/HT471

from this same Recovery you can re-install your macOS on top of your existing macOS in an effort to resolve your problem.

If you haven’t installed any of those “various” cleaning and antivirus files, then you are probably fine. I have seen other reports of problems with the App Store. Try restarting your machine. It may be a problem on Apple’s end. Not everyone is affected as Apple has many servers all over the world.