There is sewer gas coming out of the sink drain in the second floor bathroom…and we can see condensation or smoke rising from the main stack vent outside. If we get the vent cleaned out, would that solve the problem?
Sounds like venting problem. If you see condensation coming from the main vent stack, it probably is open. I’d be more suspicious of your bathroom sink(lav) vent. The lav drain should have a “P” trap installed to prevent sewer gas from entering the building. The trap holds a water seal blocking the passage of gasses. If the vent serving the lav drain is not functioning properly (or if there isn’t one) the water draining from the sink will siphon the water from the trap, leaving an open airway from the sewer pipes and drain lines.
AND, you solve the problem by looking for an inch and a half or two inch pipe coming through your roof directly above this bathroom. Get on the roof, clean out any debris (leaves, pine needles, bird’s nest, etc) you see, and then run water from a garden hose down the vent.