Glenn Herbert

There is no point in using stainless, let alone triple wall, around the riser to hold insulation. Simple black stovepipe will work fine for little cost.

I would advise using rigid insulation that will hold its shape when the steel riser burns out. Steel in a burn tunnel and riser will corrode quickly when the fire heats it to cherry red for hours per day. If you do not insulate, the steel will last longer because it will radiate away the heat, making the combustion much less efficient and much dirtier.

A good rigid insulation for this purpose would be a mix of mostly perlite with just enough fine clay to make it hold together. Fireclay, available from masonry suppliers in sacks of powder, is the best for this purpose.

I think that is likely to work as long as the roof slope is enough for the tiles to function properly by themselves, just in case water does get through the plastic. You would be building up a thicker layer of material turning to soil if you let ivy grow over it, as that will effectively trap leaves and twigs, so make sure the framing is extra sturdy.

Considering bark thickness, I think you would best cut saplings in the 2 to 4 inch range for RMH fuel. This will still give plenty of small stuff for kindling, and larger logs up to 3-4" burn great and last longer than tiny sticks, and do not build up thick coal beds since they keep their shape without collapsing longer than smaller wood.

Black locust is an excellent firewood and coppices well. If you can dedicate an area to it, it will sucker from the roots and fill the area with easy to harvest trunks. Keeping it away from lawns or places you absolutely do not want trees is a good idea.
It does grow short fat thorns on small branches; these fall off as the trunks get bigger. Honey locust gets huge complex thorn clusters on larger trunks, such that it is a danger to tractor tires.

Willow would coppice fine and is easy to harvest, but is very light and has little fuel value for the volume.

Ash coppices beautifully and is easy to split, but unfortunately the emerald ash borer is or will be killing it off everywhere before long.

Freezer panels would be completely wrapped in metal (or other waterproof material), but since you have cut holes for electrical fixtures, I would expect the white piles to be from mice making homes inside the panels.  Are the piles near panel cuts? Are they under furniture that could be chewed into? Mouse droppings and dust from them could be an issue alongside mold, and would support mold growth. How well have you sealed the places where you cut into the freezer panels?

You mentioned putting a layer of black plastic under the holey roofing and above ceiling panels; can you see into that area anywhere to find out if the plastic has been damaged and possibly leaking into the ceiling? That might give habitat for mold.

Finally, assuming you can get the walls sealed or reworked to not give problems, a rocket mass heater would give you an excellent source of free durable heating. You have lots of cob material and fuel at hand. Building a basic 6" J-tube RMH with a bell could be done with some salvaged old bricks and a barrel, and some stovepipe for a chimney. If you can afford firebricks this year, you can make a permanent RMH now; if not, you can make one for no money that will last a few years until you can afford nicer materials.

Weight for a rocket mass heater could be anywhere from 500 kg to 2000 kg depending on the space and the system, and the climate.

In an apartment in the middle of a building in Athens, you would have a Mediterranean climate so not deep cold, and no roof heat loss, both calling for a smaller system. What is the usual day/night temperature in the winter? How big is your apartment, and how much outside wall do you have? What direction does the biggest wall face, and how much of the walls are window area? I would guess that in your region an industrial building would have uninsulated masonry walls.

I think it is likely that you could use a modest RMH and that your floor could carry the weight. An engineer's opinion would be necessary before proceeding.

I second the notion of enclosing the smallest area you can get away with for this winter. Plan for the future and do a comfortable layout next summer.

I like the roofing nails as plugs to glue into the .22 holes in the roof. I would suggest to nip them all to 1/4" or so before putting them in place... much less effort to end up with non-dangerous interior.

Rather than mostly filling the bottom barrel with clay pellets, I would put a couple inches of insulation (perlite-clay) or some CFB around the burn tunnel but otherwise leave the inside of the barrel open for freest airflow. You want a sturdy layer of cob all around your feed tube so the bricks don't get knocked out of place, and I think you would benefit from wrapping the whole bottom barrel with cob for stability and heat storage.

Nice work! I think you will have a heater to be proud of.

The rockwool when mixed into clay/mortar will lose any insulating value, but it will nicely replace the straw in cob and reinforce the riser coating.