I would suggest getting APK files from your favorite APK website for the apps in question. Also, try updating Google Play from the Google Play store, NOT Apkmirror. 
Not to mention the obvious stuff such as force restarting google play services, or restarting your phone.
You could also just give it a while. My phone does something similar where it will get stuck at 100% and will take a while to go to installing. Good Luck!