Well look at the vent ( exit ramp) a laying hen will have a large moist pliable vent a rooster or pullet not laying will have a small tight opening . I suspect you have other chickens that are laying .
I have no complaints about the trigger speed . On rare occasions I get a empty pic . Running game is hard to get a picture of on any camera . Depends if you point it down a trail or across the trail and if the animal approaches in the predicted direction .