First things first, and I will make things as simple as I know how to.
The second largest appstore is called UpToDown.
There is an app, but you can also use the website:
https://en.uptodown.com/
Touch the magnifying glass to open the search function.
Enter 'Google Play Services' and select the multicolored puzzle piece icon with that name.
Touch the three dot icon on the upper right, and select 'Versions'
Select the top one.
It will download and then select 'Install'.
If you haven't already, a toast message will pop up asking you to allow 'Install apps from unknown sources'. Check yes, make the setting adjustment, then install the app.
After that, go back to the search icon and enter 'Google Play Store'.
Select the multicolored arrow pointing to the right with that name and do just as you did above.
After it is installed, do this again for an app called 'Android System Webview', the icon is a white pinwheel.
Once this has been installed, go into your Settings and select Apps.
Select All Apps
Find Google Play Store, and select Storage.
Clear the cache.
Now back out to the Apps and find Google Play Services, and clear the cache as you did above.
Now open your Google Play Store App and try it again.
This sounds elaborate, but these three apps have all been recently updated and are essential to your device.
If for some reason you still have the same issue, go back into your Apps under Settings and clear the Data for both Google Play Store and for Google Play Services.
Google Play Services will only allow you to 'Manage Storage', so just clear what you can.
Now open Google Play Store again and wait about five minutes or so.
Be sure to check all of your settings, because a data clear will cause them to revert back to default.
Try to download your apps again.
UpToDown is a nice appstore, and so is ApkPure.
https://m.apkpure.com/
Both allow you to download older versions of apps, and often times if Google says that an app is incompatible with your device, you can get it from one of those two.
I use both of them, along with F-Droid- instead of Google Play Store.