Both have been discussed here many times, and the range of opinions is wide. It's probably best to limit any additional foods pretty severely when they are very young, to prevent crop and digestive problems, and to insure they get a well balanced diet. As they mature, diet can be more varied. A mother hen takes her chicks outside at 2 or 3 days, but they have the mama to run under for warmth. Many experienced chicken keepers never have the chickens in the house at all. Chickens can definitely live outdoors in most any weather (maybe not northern Alaska) at 8 weeks, and again, experienced keepers often put them in a coop without added heat at half that age or even less. If you take them out for short outings and have a large enough brooder that they can get away from the heat entirely, you will learn to tell by their behavior whether they are comfortable.
I brooded my last batch in the coop with a heat lamp, and lots of hay to snuggle into. By 3 weeks the chicks were staying away from it, even to sleep, so I turned it off. I don't remember what the outdoor temps were exactly, but it was spring, so likely a 50-80 range.