MicroG pretends to be the Google play services to keep Apps that are dependent on it working. Even Aurora can not tell that you don’t have the Google stuff, so it offers you updates for it. You should therefore just ignore them. It is best to just blacklist Google Play Services in Aurora, then you don’t have to think about it again
Applications in Apps are often outdated, because the service is fetching the apk and saving them in a server outside of google, so you don’t have to make requests to google for updates. Aurora on the other hand downloads directly from google, so you have the latest updates.
Aurora sends a list with the package name of all your installed app to see if updates are available. As apps on Aurora and Apps have the same package name, Aurora will show updates form them.
But you cannot install update for applications downloaded in Apps from Aurora: Android will detect the installer source is different (Apps vs Aurora), and will reject the update for security reason.
You have 2 options:
Update the applications with Apps and blacklist them in Aurora (Open left drawer then click Blacklist manager)
Uninstall the application downloaded from Apps, and install it from Aurora: you will then be able to update it with Aurora
What I do is blacklist in Aurora all apps I have not installed from it, so it stops annoying me.