I believe that the blocking that you are looking at was installed as fire stops/ solid fire blocking, that being a way for a fire to be delayed within the wall of a balloon framed structure, which is when the framing wall studs go thru from the bottom of the house all of the way up to the roof. It would also be added to the framing to strengthen the wall from twisting while the green framing lumber dries out.
If you are asking about building some sort of storage thing into the wall cavities, remember that you will be using usable insulation space and should consider some sort of rigid insulation behind this thing that you are building, assuming that it is on an exterior wall.
as far as cutting this wall to enlarge openings, you might consider using some sort of Simpson strong tie hanger to carry a header from stud to stud.
I know that they make one that does not have the nailing flanges, to allow you to frame flush to your existing wall surface, kinda of a U shaped
fabrication that screws thru the back of the hanger, then you drop your header down into it. Add Jacks or blocking under this after installed and you should be all set to go, I wouldn't suggest opening up the wall more than tow cavities wide though without transferring carrying weight all the way down to a bearing surface, such as top plate or footing.
Hope this helps