Marda has the right idea. You wouldn't want to cook everything together from the get go, because by the time the chicken is cooked through then the veggies will be mush. Either cook the chicken most of the way first, add the veggies and finish it all together... or, cook the veggies first, remove from pan, cook the chicken through, then add the veggies back to the pan. With cross contamination, you really only need to worry about that if you will not be cooking the food (i.e. chopping veg for a salad with same knife used to trim raw chicken). As long as everything is cooked to the proper temps, bacteria should not be a problem. For the potatoes, it depends on the size of the dice and the cooking method, whether or not there is a liquid, etc. I'd plan on 10 to 20 minutes. Happy cooking!