Do any google apps have any special privileges that normal apps don't have?
Google's apps don't have any special privileges just for being from Google.  But certain permissions are only available to apps that are preinstalled on the device (as opposed to installed later by the user), so some of Google's software gets special privileges by virtue of being preinstalled.  On something like a Kindle Fire, which comes with Amazon's services installed instead of Google's, Amazon's software would get those special privileges instead.