If you are having trouble with the Play Store seemingly not downloading apps, either with an odd error message or just putting all your downloads in a queue rather than actually downloading them your device may have missed a Play Store app update. You can check your device for which version of the app is installed with your app manager. Each device has different steps to access the app manager.
Next, visit this site:
Search for the app you need, in this case, Play Store and snag the latest version. Then do a manual install. You might need to disable certain security settings temporarily to run the installer.

Also, if you want access to the latest versions of Android apps, this site has many of them as well, some of them even in Beta stage.

On my previous (LG) phone I opted to visit the site on a PC Computer, download the app then drop it to the download folder on the phone via USB cable. This seems like the logical choice anyway because in the case of this phone the downloader was broken.

I have seen identical issues with many ZTE phones out of the box. The voice search on google fails, the software updater fails, the Play Store does not download anything.

This site does not screen your device so you may download apps that are not compatible with your device. Peel remote is fantastic on a phone with an IR Transmitter but try it on one without one. It will not crash your device, just look like it is working and do nothing.