your pickup radius should exceed the fire area such that if food falls in the fire from the cooking rack, you can just drive by and collect it. I have this problem all the time with my current kitchen. As for the cauldron, this sounds like your smoke isn't vented properly. I have not had any trouble with it at all,: the cauldron does not block smoke and make it do anything other than go straight up.
cooking fires and smoke should not kill you even if you are not eating at home. But I can't recommend enough eating at least 1 food at home, whether its just lizard tail or grilled deer, honey, jerky, or other total crap. The difference is that you don't heal without at least a little something, so slow attrition of smoke etc can get you over time.