So my house was built in 1957, I have shiplap siding and behind black boards that are fireproof.
On the photo you can see the exterior wall where these boards are. Should I use unfaced insulation or faced ?
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If it were my home, I would use paper faced batts, with the stapling flange set to the side of the studs, so the edge of the flange is flush or near flush with the face of the stud. Insulation that needs to be cut, cut it 1" longer than the space so it fills the cavity completely and give a stapling edge for one side. At the top and bottom, it will certainly fill the cavity there, giving that little extra in length.
If the stud cavity is 3 5/8" deep, you could fins R-13 insulation to go in there. Compressing R-19 will waste money thinking it will give better R value. If the cavities are 5 1/2" deep, then by all means, use R-19.