I asked no question for you to answer, save the one you actively and at not obviously needful length failed to treat at all. How do you propose to power an electric arc furnace on peat, coal, or hardwood? How do you propose to produce liquid oxygen with like premodern fuels, which the problem statement declares as a constraint? Save the trivial point that less useful metals with lower melting points are easier to work, what does any of what you've said have to do with anything I and my prior interlocutor actually were conversing about?
That last question, though at least actually asked, also requires no response. Its answer is obvious, also trivial, and unrelievedly in the negative.
I suspect you and I share similar pessimistic views of what a post-industrial, post-carbon, post-collapse scenario might be capable of. I was amending and supplying technical corrections to your points, though I agree generally that landfills won't come close to replacing historical raw material sources.
Addressing the question of metalworking and presuming a rubbish tip source, it's useful to note:
- Previously refined metals won't need refining or smelting but rather recycling. This generally simply requires heat. Aluminium does not, for example, require (electrically-driven) reduction, iron and steel do not require (coke, oxygen, or hydrogen based) carburation. The heat requirements remain challenging, but it is still a lesser challenge than production from ore.
- There are conceivable thermal processes which might assist, and for which technological knowledge even in the absence of prodigious energy resources might suffice. Solar thermal energy (requiring polished mirrors, but these being reasonably attainable) can achieve temperatures of 3,500 °C (6,330 °F). Steelmaking "only" requires temperatures of ~1,700 °C. Total capacity of a solar furnace would be well below that of a fuel- or electrically-powered blast or arc furnace, but useful quantities of metals and glass could likely be produced without extirpation of forests for charcoal.
- Siting near geothermal or hydroelectric resources, and presuming electrical generation, could enable electric-arc furnaces. Even today much aluminium production is opportunistically sited near such cheap power sources.
Several of these options might not be immediately available following a widespread collapse, but could be bootstrapped within reason over time, though most likely at far lesser scales than at present.
My suspicion is that a post-collapse society, and/or a future technological society operating with a rewewable energy basis (biomass, hydroelectric, geothermal, solar, wind) would probably have very different material bases (far more stone, brick, and ceramic, some plant-based materials whether structural timber or plant-fibre-reinforced ceramics), a vastly different land-use pattern (concentrated rather than sprawled settlements) and transportation (water-borne, canals, heavy reliance on pedestrian travel, possibly electric-powered transit and freight, minimal air travel). Overall energy-intensity comparable to the late 19th / early 20th century in the US and Europe may be reasonably attainable with smaller populations, and on balance that wasn't particularly burdensome. Food production is probably the major hurdle without Haber-Bosch ammonia production. Sufficient farm mechanisation given some available fuel and/or power distribution (alcohol, biodiesel, possibly synthetic hydrocarbon production, elecricity) would have a huge societal benefit even at small fractions of present total and per capita energy usage, not just for agriculture but other high-benefit uses such as marine propulsion and remote heat and power.
This is a discussion site, and the discussions occur between more than just two people (e.g., comment and response). I was responding with additional context for any reader interested, though of course you can be presumed to have interest. Discussions are not however proprietary, and shouldn't be treated as such.
That last question, though at least actually asked, also requires no response. Its answer is obvious, also trivial, and unrelievedly in the negative.