For the boxes, it's just luck of the draw. And it sounds like you've been dealt some bad hands. As per weapons not doing enough damage, what weapons are you using, does the enemy have armor, where are you hitting them and are all of your shots connecting? With a semi-auto rifle I usually shoot for center mass and it takes three shots on an unarmored target. With a hunting rifle I believe it takes two to the chest. Burst rifle I'd say is two bursts and the bow is two arrows. With sidearms I just shoot till they're dead.
For the week resetting part, I can't help you. Try not to exit mid-game maybe?