Insulation exposed behind face of the fireplace

This is sometimes rock wool insulation. Even if not, fiberglass insulation is non-flammable, as long as no vapor barrier is used with it.

Installation of fireplace doors and fireplace inserts usually includes such insulation.

Did the transparent glass "back wall" explode because you added the front side glass doors and as a result the temperature in the fire box area went way up???

You need to consider carefully the airflow and draw requirements of the fireplace and the chimney that vents it out through the roof. Changing the design can really change the temperatures of the internal space!!

I would think that if you were to block off the far side with bricks that you may need to line the inside of the brick with special heat resistant fire bricks. Regular bricks could get extra hot and shatter too.

If you really need to have the front side glass doors make sure that there is a part of the design that permits the proper amount of air flow in around the sides of the door assembly for the chimney draw to work correctly.