I'm trying not to answer all the questions, I would like other folks to get involved somewhat.
The first step is to support the framing underneath. Any blocking installed there is going to help more than anything you do on the top. The top will work fine with some 1/2 inch wonderboard or cement board with whatever bonding mortar you want to use. I would use what the company supplying the stone recommends. Some stone is more porous than others, depends on where it is from sometimes. I would leave a 1 inch finished overhang at the edge, don't forget to add for the thickness of the material underneath.
This should also be inspected by the fire marshal, if you do not , your insurance co. may not protect your assets if there is a problem. This means Fire or carbon monoxide poisoning.
Enjoy your fireplace, it sounds nice.