In "The Sniper", what happens after he fires his weapon?

It depends upon which time he fires his gun. At the beginning of the story, the sniper is fired upon by his enemy because his enemy sees his cigarette smoke. An armored car approaches and a woman informs a soldier in the armored car of the sniper's position. To protect himself, the sniper shoots the soldier and the woman. 

The enemy fires upon the sniper again, this time hitting him in the arm. The sniper comes up with a plan. He puts his hat on top of his rifle and raises it up. The enemy thinks it is the sniper and fires. The sniper drops the rifle, giving his enemy the impression that he's been shot and killed. This is when the sniper shoots and kills his enemy with his pistol. The enemy falls to the ground. The sniper undergoes a temporary change here. Up to this point, he had been a single-minded soldier, a trained killing machine. But this shocks him. He's killed a fellow Irishman, someone close to his age. He becomes more like the innocent student he used to be: 

The lust of battle died in him. He became bitten by remorse. The sweat stood out in beads on his forehead. Weakened by his wound and the long summer day of fasting and watching on the roof, he revolted from the sight of the shattered mass of his dead enemy. His teeth chattered, he began to gibber to himself, cursing the war, cursing himself, cursing everybody. 

In disgust, the sniper throws his pistol to the ground. The gun goes off and a bullet flies past him, shocking out of his remorseful state. Once again, he becomes the single-minded soldier. Note that it is a violent act that shocks him out of the soldier-state and a violent act snaps him back into that state. The story ends with the sniper looking into his brother's face. This final line shows the tragic reality of a civil war. 

What happens to the sniper in "The Sniper" after he shoots the man in the armoured car?

After the sniper shoots the man in the armored car, he shoots the woman who indicated his position.   In order to get a good aim at the man in the armored car and the woman, the sniper had to expose himself to his enemy.  Consequently, he was shot in the arm. This endangered his life because he could no longer handle a rifle.  It was too heavy, and his arm was too weak.  He had to find a way to get his enemy within revolver range.   He knew that he could not wait until morning because,

“The enemy on the opposite roof covered his escape.” (pg 2)

He needed a plan in order to deceive his enemy.  He placed his cap on top of his rifle and held it over the parapet of the roof.  A bullet pierced the cap.  He held his hand lifelessly over the roof and dropped the rifle to the ground below.  His deception had worked.  The enemy thought that he was dead and stood up. 

“He was now standing in front of a row of chimney pots, looking across, with his head silhouetted against the western sky.” (Page 2)

This allowed the sniper to focus his aim on the enemy.  It still took an excellent shot to kill the man in the dim light with a revolver, but the sniper succeeded, and the man fell off the roof and landed on the ground below.

In checking out the identity of the enemy , the sniper realizes he has just killed his own brother. 

My copy of the story is from the internet, and the page numbers may not coincide with your version. They should be close.