Is it possible to install/update apps from Google Store via PC? A few months ago I was forced to uninstall some apps in order to update other ones. Recently I've lost the ability to receive email notifications via Gmail (searching works, however). All because of trash apps Google Play and Google Play Services, which are constantly growing. I plan to completely uninstall them, at least regaining the functionality my phone had 2 years before.

However, if I would have to do the update of some app, or I would like to install new one, is it still possible to do it via PC connection? How to download application to my PC in order to install it to my phone?

Note: I've already lost the ability to update or install new apps because of too little storage on internal memory card.
There is a Java application to do this, which can be found here. It's called the Real APK Leecher. It works by pretending to be an Android device (you need to configure it with your Playstore account data), so it connects to the corresponding Google services like any other Android device with the Playstore app installed, let's you browse the Playstore, and download APKs. I didn't try it out myself, though; but you might wish to give it a look.