Installed app is deleted from Play Store. How to download it from my mobile to PC for backup? There is an app that I have on my phone that is VERY USEFUL to me. The problem is that soon I'll have to change phone or reset to Factory settings and this app is no longer available on Play Store for download after losing it. 

Is there some way to download the program/app from within my phone and copy it for backup on my laptop? Then I'd like to put it back on my phone and be able to re-install it myself (ticking install from unknown sources I guess?) after the reset.

Can it be found on my phone and be saved?

Thanks :)
Our backup tag-wiki mentions what might help you: ADB backups. You can check with our adb tag-wiki to get an idea on it, learn more on ADB backups via these answered questions.

Then, once you've got ADB up and running, adb backup -f myapp.ap -apk com.my.app will backup the app including your data, so you can even transfer it to another device.

Not that some apps do "opt out" of this backup method. In that case, you'd lose your data, but could still extract the installation file e.g. using an APK extractor. Or if you'd not be afraid to root your device, you could use a full-fledged backup app like Titanium Backup – which not only would allow you to backup all your apps and their data, but also your settings, SMS and more.