Is there any way to update
An app downloaded outside of the Play Store can't   be updated using Google Play update mechanism, it  won't appear in the downloaded list as well simply because not  your Google account that downloaded it. 

An app downloaded from Google Play may not modify, replace or update its own APK binary code using any method other than Google Play's update mechanism.

The paid version isn't showing up may be because the developer has put restrictions regarding your country or your Android version, etc.

Update:
Try downloading your apps from a third party market such as Monogenie or Aptoide, you'll be notified whenever an update is available.