Hi, sorry for the lack of responses so far. I have just taken possession of the older house, so I don't know it very well yet and therefore cannot answer how the draft is or which way the air goes. This house is heated with geothermal energy but has a fireplace that is used in winter, so the chimney at least gets warm in winter. Generally, the house is poorly insulated, and the windows are original, so it should be sufficient from a supply air perspective. In the laundry room and bathroom in the basement, there are extractor fans, but otherwise, no active ventilation. Anyway, the point is that the ducts you mentioned as exhaust were made of asbestos cement, so we have removed them and need to replace them with something. What? The chimney has 9 pipes up out of the chimney, two larger sooty ones that I assume are for the stove and for the oil/coke boiler that was there previously. The rest are relatively 'clean', and from what I've seen so far, they go to the bedrooms and the bathroom.
In the 1950s house, it's oil-heated (rarely anyone there in winter), and there I find that the exhaust ducts in the summer (cool outside) provide supply air (also checked by holding up a match), which is why I thought it was a 'smart' solution with supply air when it's cool outside, a bit like night cooling in larger facilities. Especially since it looks like the chimney has openings both on the side and on top.
A long answer that will hopefully lead to questions and tips on what we should replace the asbestos cement ducts with. (The contractor suggested plastic spiral ducts (I would rather have metal in that case))
Thank you in advance.