Over 80 years, anything is possible. The best way to start getting an idea is with a measuring tape and drawing a detailed plan. If you end up with a big empty space in the plan, then the possibility of a fireplace exists.
Unless the former owners of your new old house used the other fireplace regularly and recently, I would not start a fire in the open one until it was inspected and cleaned/swept. Fireplaces are subject to neat things like condensation of flue gasses that leads to deterioration of bricks and mortar. I'm not saying that this has occured in yours, but it your fireplace hasn't been used in some time, have it checked since there might be a reason that it wasn't used. Birds and animals like living in the warmth of unused chimneys and starting a fire without a way for the smoke to get out is not a great way to find this out.
Your furnace and water heater need to be vented. They will exhaust combustion gasses up some kind of flue to the roof--and be subject to the same kind of corrosion of mortar. Over 80 years, the furnace should have been changed out several times. What changes were made can be investigated from the basement and it's common for one chimney to have 2 or 3 flues. When your chimney sweep goes up on the roof, he can give you more info from that end.