Most of what we learn about the man in the armored car and the old woman in Liam O'Flaherty's short story "The Sniper" comes from the narration and the observations of the Republican sniper. However, there are a few things we can infer.

The story is set around 1922 during the Irish civil war, taking place in Dublin at what is known as Four Courts. The two sides fighting are the Irish Republican Army and the Free Staters. There are snipers pitted against each other in this story, one fighting for the IRA and the other, for the Free Staters—each on the rooftop of two different buildings. The narrator reports on the thoughts and the actions of the Republican sniper. 

When the sniper refers to the man in the armored car as the "enemy" (in that the narrator has identified the sniper as a member of the IRA), we can infer that the driver of the car is a Free Stater.

Just then an armored car crossed the bridge and advanced slowly up the street. It stopped on the opposite side of the street, fifty yards ahead. The sniper could hear the dull panting of the motor. His heart beat faster. It was an enemy car.

Because the driver moves slowly, we can also infer that he anticipates some kind of trouble. He also does not move the car very far up. The driver also leaves the car running, so we can infer that he wants to make a quick getaway if necessary. We can infer that the driver must be confident with regard to his safety in that he opens up the car's turret and sticks his head out into the open.

The sniper quickly shoots and kills the driver.

Then round the corner of a side street came an old woman, her head covered by a tattered shawl. She began to talk to the man in the turret of the car. She was pointing to the roof where the sniper lay. An informer.

The sniper identifies that the woman is an informer. Once again, we can infer that she is a supporter of the Free Staters. However, we might also infer that she is not supportive of either side, but is frightened by the gunfire. We take the sniper at his word that she is an informer. She is old, which would support her possible fear. We can also infer that she is poor. The shawl on her head is tattered. Additionally, we can postulate that the shawl on her head could be either to protect her from the weather or to protect her identity if anyone should see her.

Upon hearing the report of the sniper's rifle, the woman turns to run. We can infer that she believes she is now in danger of being shot by the sniper, who does, in fact, shoot and kill her.