Quinn connects several AA batteries in series to stand in for the car's flat lead-acid battery, and while this could increase the AA batteries from 1.5V to 12V, it does not increase the amperage, it remains that of a single AA battery, so there is no way this setup could ever provide the huge current required to start a car. This is the reason cars don't use AA batteries like your TV remote.
To find pandemic survivors, the well-equipped Stalkers utilize sophisticated parabolic microphones to detect signs of life, yet since Ellie and Quinn use lamps at night and fires to cook over, it would be so much easier just to look for light and smoke, or use infrared detectors to look for body heat. Or use simple drones with video cameras to search for movement, like Ellie and Quinn riding around on their bikes.
Ellie is starving, resorting to eating cat food and struggling to stay alive, and yet rather than spending every minute looking for food, she wastes time by keeping going back to a dance studio to practice ballet alone.
Quinn has built a rocket to act as a warning flare, but since she is a loner, before meeting Ellie there would never have been anyone to fire it, and therefore no sense in having it.
Trying to hide from the Stalkers hunting them, Quinn watches them through binoculars, not from cover, but while standing dramatically silhouetted against the clear sky on a rock outcrop.