The white bricks are "fire brick", design to tolerate the extreme temps of the firebox itself. With a self-contained insert they're not necessary, but if they're what's holding up the steel angle iron supporting the rest of the brick above, you may want to cut in some steel pillars or some other mechanical support for that angle iron if you're removing them completely.
The rubble-brick jumble filler is a common way to isolate the thermal expansion/contraction issues of the hot firebox and the potentially cold/very-cold exterior to keep the masonry from cracking (either the firebox or the exterior), though filler wythes of solid masonry with cavities between them, or even solid masonry are sometimes used. Any non-structural stuff like that isn't really needed for an insert.
What you DO want to do is make it all as air-tight as possible before you button it up, since there is a significant "chimney effect" driving infiltration even for cavities filled with masonry rubble, and if there's room for it, R15 rock wool batting will limit the heat loss out the back side even further, and would still meet code. This appears to be an exterior above-grade wall, and if there is no exterior insulation (usually the case), the fireplace brick represents a big R1-2 hole in your otherwise decently insulated wall, which has both comfort and efficiency ramifications. Check the clearances requirements in the insert spec, but most don't have any problems at all being in contact with non-combustible high-temp insulation like rock wool. Many have no insulation at all, in which case more than half the heat from the insert would be going to the great outdoors, in your configuration, no matter what the efficiency numbers in the spec say.
Use sheet metal for air barriers on the masonry. The tough part to really air seal well is where the Napolean's top vent passes through your home-fabricated sheet metal top-side air barrier, but using automotive muffler-repair putty can narrow the gaps safely. Even though it won't form a permanently-perfect air seal, but even after it develops cracks it's way better than a extra 1-4 square inches of air leak with a 24/365 stack effect pull on it.