First off, you should carefully inspect the cast iron, firebricks and grates for cracks or damage. Check the grates to be sure they slide/move easily. Replacement grates are available for this stove but I am not aware of anyplace that makes firebricks for these stoves anymore.
From the description of your home, I think it should heat it ok. The living room will be significantly warmer than the back rooms.
As far as smoke coming out when you open the door/lid, if the chimney is designed properly smoke should be minimal. Generally, chimneys that run up through the inside of the house and are taller than the entire house work the best. Chimneys that run up the outside wall of the house can be a problem. You will want to use a manual pipe damper for this type of stove since you plan to burn wood in it.
These stoves were not designed to be "air tight" (no gaskets etc.) but they are still very good stoves in my opinion.
Be sure to get at least 2 smoke/carbon monoxide detectors if you don't already have them just to be safe.
Wood,nCoal is right, these stoves are excellent coal burners. If you post the general area where you live I'm sure we could help you find coal.