Do any google apps have any special privileges that normal apps don't have? Every android app has a series of permissions which is granted at install time. Some google apps seem to be able to do some pretty global things that not many other apps have (eg. google now constantly reading the microphone to hear when you say "ok google").

Just wondering, are there any permissions which only google are allowed to have or do all apps have access to all of the same permissions?

can I technically create an app with any of google's features?
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.