Can water flow through the backboiler of a stove directly into the hot water tank and back to the boiler or does it have to run through a coil? If either, what would be the pros and cons of each? If on a seperate circuit, are expansion tanks required for the hot tank and the coil/boiler circuit?
In either situation, the system is topped up by cold water flowing into the hot tank, yes? Presumably this occurs whenever hot water is run off. How is the heat then maintained if, say, all the hot water is run off in one go - surely by the time half the tank is drained the water would be luke warm at best having been topped up by the cold intake???
This is for a basic thermosyphon system with no pump or mains pressure.
I know there are a lot of knowledgeable people here who I don't wish to annoy wth idiot questions! There seems to be a shortage of basic information online however so hopefully my questions will also be of benefit to others at some point...
Thanks...

First set of questions -- can be done either way and I'm not going to discuss the pros and cons. If on a separate circuit the boile-tank coil circuit needs an expansion tank. If on the same circuit whether you need any expansion tank depends on whether "mains" or a pump with a check valve. In the latter case you need an expansion tank but in the former the pressure cannot rise above mains pressure (expansion water can flow backwards toward the mains).

Second set of questions --- the cold water feed for either mains or pump is to the bottom of the hot water tank and the hot water outlet is at the top. Because the cross section of the tank is huge compared to the pipe diameters the vertical flow rate in the tank very low. Hot water is less dense than cold (above 4C* this is true) and so as a hot water tap is opened, the pressurinzed cold water enters at the bottom forcing hot water out the top. Won't mix that much until you have used most of the hot water. Or rather, won't mix quickly (in spite of the density difference, if no hot water used and no heat input to the tank, after a few hours the water in the tank would be lukewarm). If you are using the hot water reasonably fast (say a shower) then when the temperature coming out the tap drops you have used up all the heat in the tank. It won't gradually go to "lukewarm" but will transition fairly rapidly from hot, to a brief period of lukewarm, then dead cold.

* Water is one of the stranger substance in the universe. It has a positive thermal coefficient above 4C (acts like a normal substance) but below 4C the coefficient is negative. That's why ponds freeze from the top down. As winter comes, gradually the water temperature of the entire pond drops to 4C and then as the pond loses more heat the colder water is on top (it can freeze) while below the water still unfrozen stays at 4C until the pond freezes to the bottom (which it might do if shallow).

Thanks, that clears that up nicely. I had totally overestimated any mixing effect.
With regards direct/coil heating, I wonder if anyone would like to detail the pros and cons? Seems to me the coil method would be less efficient and, if requiring an additional expansion tank, more expense and complication to set up.....??

I would say the primary distinction would be the material your boiler is made from. If the stove has a stainless steel boiler it would be suitable for direct use but if steel or even a cast component, then indirect heating is best. It keeps the rust out of the hot water, allows you to use an inhibitor to prevent the rust and will also mean the boiler lasts longer I'd imagine. I don't think the efficiency difference is as much as you'd imagine. The boiler coil in my cylinder is rated for 30kw though on what basis that's calculated I don't know...

And now to contradict myself: I know older AGA/ Rayburn installations are usually direct though I believe their boilers are mild steel...