Not sure about the Durock or wire mesh, which is one of your main questions. I don't do tile work, but I do design fireplace covers and gas fires and often help people with an overall finished look.

So I created these two mockups to help you along the way, seeing as we don't know what direction you are really going with the style of decor in this room.

I was going to create a mockup also showing a more traditional style mantel surround, but ran out of time. If you go that route, those two electrical supplies will likely need to be moved.

Tile floor to ceiling with glass doors and burning glass with geoshapes

Tile half way up with glass doors and matching metal angle iron trim to hide the exposed tile edge. We can make that metal trim any depth necessary. This works well if you want a rather contemporary look. You can also use wood molding. (Shown with gas burning fireballs.)

Thank you - in the designs shown, will the metal immediately around the fire box become hot to the touch?

Yes it would, just like any fireplace screen would get hot when you have a fire burning. Just so you know, the mockup shows glass doors, which always have some type of frame. But, you cannot burn a gas fire with the doors closed like I have shown in the picture. I just cannot easily create a mockup showing the doors open.