Technically, Google Play can update apps if they meet certain requirements, but Google Play cannot uninstall apps without permission. You'd be prompted by the OS to allow the uninstall if Google Play tried to do that.
If the app's signature on Google Play doesn't match the other releases' signatures, then Google Play cannot update that app. It's possible two versions would be using the same package ID and signature, but that's all on the developer for doing it that way.
unseenpolar If the above is true, is it better for privacy and security to download all other apps from the Google Play Store?
I don't think it matters. If you have Google Play already installed and use it to install one app, then I don't see the point in not using it for the other apps since, as you already pointed out, Google Play can see what's installed anyway.