What's above when you open the door? Closed box or can you see up the chimney?
Not too knowledgeable on how chimneys are built, but if you have any concerns about the condition of the chimney, get it inspected, especially if there's no liner in there. Reason being is that without the liner, there could be condensation issues especially if a mid efficiency furnace is venting into it. The exhaust of the mid efficiency isn't diluted (but may be indirectly diluted with a natural draft water heater venting air 24/7), also cooler than that of a low efficiency furnace.
I don't think you have a liner given that there are two pipes.
Not too knowledgeable on how chimneys are built, but if you have any concerns about the condition of the chimney, get it inspected, especially if there's no liner in there. Reason being is that without the liner, there could be condensation issues especially if a mid efficiency furnace is venting into it. The exhaust of the mid efficiency isn't diluted (but may be indirectly diluted with a natural draft water heater venting air 24/7), also cooler than that of a low efficiency furnace.
I don't think you have a liner given that there are two pipes.