Repairing old stone walls you are sure to find internal voids. This is because mud mortar has washed away over generations. 
Even with a newly built stone wall there inevitably occur voids in the mortar (too large areas), between facing & bond stones.
These voids must be filled with carefully chosen slim pieces of stone called hearting. This is literally the heart of a good wall.
Hearting stones, or cloch feidín, are typically made on site by breaking larger rocks into various size wedges. However on an old site like this, plenty such stone already exists. Poor quality stone walls can be identified when the builder simply pours gravel into the voids.
Voids should be tightly filled with smallish stones. 
The tighter the hearting, the stronger the wall.
Hearting stones are much better if they are flat or angular, and should be placed individually. Make sure each course (row of stone) is completely hearted before beginning the next course.
No proper hearting allows stones to move independently of one another, resulting in a structurally weak wall – that will not last.
limewindow 
Interesting – great photos
In the first pic, could it be that the space was intentional for some forgotten purpose, a drain perhaps? It looks too neat to be a defect or failing of the wall’s construction.
Def not a drain: simply where loose face stones were removed, revealing loose inner fill and a deep hole where mud mortar had washed away. Significant amounts of mortar and smallish stones must be packed in here.