Both my grandmother and my mother cooked on coal fired kitchen ranges. The area just below the lids is the fire box, at the bottom of the fire box should be the grates. These rotate so that the ashes can be shaken out to fall in the ash pan below. The reason the chimney is in the back center of the stove is so the heat from the fire will flow over the oven to heat it before it exits the stove. The pipes inside the fire box are to heat water. They are usually connected to a large tank [100 gal or more] and it usually in another room, this way there is a place to store heated water and also heat the other room.
To cook on a stove like this----just before cooking the grates would be shaken to get some of the ashes out----- a shovel of coal would be placed on the hot coals-----the drafts would be opened so there would be a very hot fire----much like OBG would do with his steam tractors. To regulate the cooking temperature ----the cooking pans would slid across the stove to the correct heat you would want to cook with. I don't remember how they regulated the oven temp----I sure it was a challenge to have baked goods come out perfect.
As far as needing another stove for heat---my grandmother kitchen was 20 X 20 and it was usually about 80 deg there when she was cooking.
As a side note when my grandmother was in her late 70's family members decided she should have an electric stove-----she never used it--put a towel over it and used it as counter space.