Would authorities in some countries take issue with his shooting the criminals and charge him with murder?
yes of course they would over here .
Well actually no , they might if you shot a robber , then beat them with a stick until you fracture lots of bones including the the skull , then drag them across the road and dump them over a wall , then return to your house for more ammunition and go out and shoot them again just to make sure , but that sort of thing ends with a charge of manslaughter not murder .