why does the sniper kill the old woman and what happens to him after he kills her ?
The sniper, from The Sniper by Liam O'FLaherty, kills the old woman in the street because she is pointing out his position to the other side. She is an informer. Because she is putting his life in danger, he shoots and kills her. This is war, and even cilvilians, like the old lady, are fair game.
Immediately after he kills the old woman, another sniper on a rooftop across the street knows his position and fires. The sniper is hit. He is shot in the arm, which renders his arm useless.