Glenn Herbert

I think vermiculite is more compressible than perlite, so if you want to use it for a loadbearing base, I would add a bit more clay to the mix to stiffen it.

It would probably be best if you can go out far enough to clear the soffit, then vertical all the way up. If you have a tall wall (two stories or more), this might not be practical, and then, as has already been mentioned, use the smallest angle possible for offsetting.

That really depends on the character of the stone you have available. The smoother and rounder the stones, the less capable they are of forming a sound wall. You will benefit most from the stone being on the inside of the insulation layer. If the insulation is inside all the stone, the stone mass will stay cold all winter, and any solar heating will be hard to transmit to the interior. If you want the appearance of a stone building and the benefit of thermal mass, you pretty much need to have a double wall with insulation in the middle. This is assuming a climate with real winter, and the possibility of long periods with little sun. If you have a lot of solar gain and little cold air exposure, or cold only at night with sun all day, you can use a monolithic mass more effectively.

You can't have copper exposed to rocket core temps - it won't give off fumes as such, but will soften and melt; any joints inside the core would be destroyed at much lower temperatures. If the copper is carrying water, the water would flash to steam and explode with any hiccup in flow rate.

I would not just run water to the exterior wall, I would run it to all the places in the house that want warmth, with radiators at appropriate places. Or is it just one big room you want to heat? Running piping in the floor will give gentle radiative warmth, as long as your building construction is compatible.

Air ducting sufficient to heat your house will be pretty bulky, and insulating the stretch between shed and house would make it even bulkier, and may be considered by an overzealous inspector as connecting shed to house and knocking you out of compliance. After all, if a lot of air can move into the house, so can flames (the fact that you can't get flames into the duct if it is properly built is irrelevant.)

Maybe you could use water as the main heat transfer mechanism, and have an enclosure with fan to push what heat escapes the mass into the house? Much less air volume needed, and if positive pressure is required, no need for return ducts...

Note that the diagram says that C can be less than OR EQUAL to A and F... just not larger.

If you want to move warm air, I would recommend building an enclosure all around your mass, insulating that very well outside, and running the duct to your house; also a similar duct low from the house back to the base of the mass enclosure, You will likely need to situate the whole heater shed considerably lower than the house if you want heat to flow without added fans.

I think heating water or antifreeze would be more practical and work better, requiring radiators or convectors inside the house, but much more flexible in layout and less space-gobbling. I would use a large unpressurized tank sunk into the mass/bell, with a coil of copper pipe submerged in the tank and circulating to the house. This will avoid the risk of pipes bursting from steam explosions.

If you want to use a smaller drum, you can set the base of the drum on some layers of brick to raise the top to the height you want. You just need to make sure there is enough space around the riser for gases to flow freely - the free drum cross section space should be at least 2 or 3 times the system size.

If your chimney is that tall and in the center of your house, you will probably get better draft from it than you expect.  I would not hesitate to design a 12-13 cm J-tube for that situation, a 15cm might work but I couldn't guarantee it.

A J-tube core is ideally the same dimensions throughout, but if the burn tunnel is a bit smaller, that is okay. So make it all 15 cm square. The riser can be 15 cm diameter and work as well, since square channels have about the same capacity as round of the same diameter due to poor flow in the corners.

I have a 7" wide x 7 1/4" high burn tunnel and feed tube, and a 7 3/4" diameter riser that is several inches shorter than optimum, in a masonry bell, leading to a 6" diameter temporary stovepipe that is only 12' tall above the feed level. It drafts fine.