Mark, thanks so much for your answer and questions. To give you some more info (and excuse the terminology.. I am a novice!). From what I can see by the water heater, there isn't a circulator of any kind. Pretty much what you see in the photos is all we have. The green thing going to the boiler is a Taco boiler feed valve and behind the flue is a check valve on the 1/2" line pointing ->. To the left of the check valve is what I believe is the 1/2" valve to turn the thing on and off... I tried for half an hour turning it off and it just keeps twisting. My guess is it is indeed faulty.
As for turning off the faucets, I gave that a go (all of our sink faucets are two handles - hot and cold), but that didn't fix the problem with the showers. The showers are single handle Delta faucets. I also tried turning off the supply to the washing machine to isolate the problem (in the event of a faulty valve), but that also didn't fix it.
Interesting what you say about the return line. Not quite sure how to determine 100% if it is a return line, but I am pretty certain there isn't a circulating pump by the water heater.
Now, I have spent a fair while trying to diagnose this problem with you awesome experts and on another site, I was given the following advice by a couple of other really helpful plumbers:
"Disconnect the 1/2" line from where it is, pipe it to the HW tank drain, or just disconnect it and cap it, if you do go the HW tank drain you will have to add a "T" and a valve at that location.
The idea of a convection return line is cold water falls, and it should return to the bottom of the tank."
So, not sure what you think, but any feedback you can offer would be much appreciated
I think along with the above advice I will also have the water heater replaced and the flue pipe properly fixed.