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.
When the Stalkers capture Ellie and drive off with her, Quinn runs away into the desert, stopping to admire a pleasant lake view and contemplate her relationship with Ellie. Deciding to rescue her, she starts to walk back then breaks into a jog, and even though they have been driving away at some speed, Quinn on foot is somehow able to get ahead of their van and signal them to stop.
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.