How can I receive updates to .APK — program I manually download outside Play Store in Android?
If the Play Store can detect updates for that application, odds are good that you do not need to install that application from outside the Play Store. What I mean is, if the Play Store detects updates for a given app, why not just use the Play Store? Hovsep's answer is correct for applications that you've installed from the Play Store, however not all side loaded apps will be linked to the Play Store for obvious reasons. This is where third party software again, comes into the equation. There are plenty of third party apps available specifically for managing the updating of side loaded apps (which I've listed below).
Being the minimalist, install as little software as I absolutely have to kinda guy that I am, I would periodically perform a search on all the side loaded apps that I installed (if I did that sorta stuff) and then compare version numbers. If an update were available for a given side loaded app and I really wanted that newer version, I would backup my previous version (in case things get dicey), download the new updated APK file, say a prayer, remove the previous version and then side load the updated version back onto my device.
I've listed a few below (may require root privileges).
App Update Notifier
Update My Apps
Titanium Backup (has integrated third party market listings available)
as you stated perhaps not all side loaded applications will be detected, i think shareware applications will do that and particularly the games that need to download extra packages, because google play will detect that and if not officially purchased then download of extra package will fail.
your mentioned applications can cover the need of updates:)
Update apps on your device