Dormer Insulation

We are trying to bring down our gas bill. I found out the electric company offered a free energy audit, they came out with a thermal camera. The camera showed blue in the area of the dormers that are flanking either side of my kids' bedrooms. The house is barn shaped and the rooms have cathedral ceilings, so the the sides of the rooms have knee walls with attic space behind them. We opened up two of them, they both have insulation, one had one piece that had fallen. I attached pictures for reference. The wall you see without insulation is an interior wall overlooking our living room. Should it be insulated? Should the floors be insulated? What about the tiny triangle areas on the other end wall that don't have insulation?

 

It looks like the bottom of the roof is insulated. So that means everything within that envelop is within the insulated space and does not get insulated. I'm assuming that the knee wall is also NOT insulated. If that is the case the pie shaped wall to the living room should not be insulated. The benefit of this method is the attic space is within the insulated envelop and somewhat climate controlled for storage.

I prefer to leave the roof uninsulated so the attic is cold. With that method all the floor and walls adjoining heated spaces are insulated. This method essentially shrinks the size of the insulated space which can help heating and cooling bills. This also means the attic will fluctuate wildly in temperature and is not the best for storage.

 

With insulation neetness counts, I see some areas that are not "neat" the paper flanges missing/torn/unattached. Each of them a potential gap for heat to escape.

And I also have rooms with similar knee walls. Blown in insulation between the attic joists and knee walls uninsulated. I know it doesn't add much, but I insulated all those interior walls, and floor. Insulation is cheap, energy isnt, it's easy to do, and after 15 years I'm sure it has at least paid for itself!