Question: On average how long does it take Apple to update/publish my new app/update on the App Store and iTunes website?

Answer: 
It depends on a human at Apple reviewing your app. If you'd made a few small graphics changes then it won't take very long, if you've added stuff like access to the address book or whatever they may look more closely. And it may take a while for them to get to yours if lots of other apps have been submitted recently too. So you might as well ask "How long is a piece of string?"
usually around 8-10 days from what I've experiences (and according to this site)

<http://reviewtimes.shinydevelopment.com>