This was the vid I followed to root mine. His site is a fund of info on all things Note, Note 2 and S3.
https://www.youtube.com/watch?v=DwsIjw2yPRs
Once done I renamed /system/media/audio/ui/shutter.ogg to shutter_old.ogg as a test and it went fine. I'll replace it with something less intrusive when I find a nice sound.
x-plore is a great file explorer for things like this. You need to change its settings to allow root file changes then SuperSU will ask if you want to grant it root access which you can do as a one off or indefinitely.
Edit:
There are a few free tether apps out there that don't require root.