Even though there's almost no way of determining equivalent cost between the middle ages and the modern day, I thought that equipping a knight was equivalent to $1m in terms of materials and skilled labor.

Steel no. Bronze and copper were frequently used to plate gates. Partially decorative, partially to make it harder to cut through or burn down the gate.

There are two uses of metal in fortifications prior to the invention of large scale steel smelting in the 19th century.

1. Iron cramps were sometimes used to hold stones together more solidly (or as reinforcement while the mortar dried. Medieval mortar was wetter and dried more slowly than modern mortar, so this could take a lot of time). Especially in arches like at the top of gates, in bridges etc.
2. Gates and portcullises were frequently ether reinforced by metal or plated with metal. Sometimes this was purely defensively, but often it was decorative as well (displaying the wealth of the city or lord that owned the gate). The gates of Indian fortresses were also frequently studded with metal spikes to prevent an attacker from using elephants to bash down the gate.

The Bessemer steel making process was developed in the mid 1800’s. Prior to that metal working was a specialized task suitable for individual weapons and armor but didn’t scale up to the volume needed to fortify a castle or other structure.

Siege engines were routinely covered in metal to prevent the enemy setting them alight. The colossus of Rhodes was said to be built from the metal from captured siege engines. https://en.m.wikipedia.org/wiki/Colossus_of_Rhodes

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You have to consider that all metals at the time were produced by hand and forging large sheets would have been next to impossible. Much cheaper just to go thicker.

I remember this being done all the time in the 90's then it simply stopped. One would think that with the advent of 3D printing it would come back with a vengeance. Wish it would.

Metal staples were used in masonry as well to hold casing stones tight and in place.

Castles have some iron fittings e.g. portcullis spikes, sconces etc. In order to plate wall with metal that could withstand e.g. a trebuchet or ballista you're talking battleship thickness. Stone and timber were much cheaper and easier to transport for repairs. Considering as well a suit of armour would have cost $100,000 in today's money because metal wasn't mass produced it wouldn't have been economically viable to plate a building and good luck finding enough ore without modern mining methods.

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Like the answer for the descendants of Charlemagne, the answer is technically a yes, after countless generations of intermarriages, the genetic heritage will spread to a given size of the population. It is possible that even today there are those who still bear the heritage of the royal house, though they would likely not be of any significance . Even the Aisin Gioros are now little more than salarymen. It would be impossible to trace a specific lineage that far back with complete certainty. No record has lasted that long. So no, there is not some secret elite family like with the ex-royalty of Europe that we could confidently consider to be the continued direct familial legacy of the Shang.

One interesting point is that the traditional Chinese accounts actually had the succeeding Zhou dynasty appoint the Shang as dukes of a small fief rather than outright purge them, so this lineage supposedly survived long enough to produce some of the dynasties of the various kingdoms that emerged during the Zhou's collapse.

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There were many Roman camps and settlements in Spain. Some have kept their names, for instance Zaragosa is the current iteration of a Roman camp named after emperor Caesar Agustus (zar-agosta).

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Interestingly enough the US nearly "lost" the location of the battlefield that won it's independence from Britain when people wanted to build golf resorts over it.

How many Roman ruins have been lost because some farmer uncovered one and went “Godammit, not another one. Someone get a hammer, I’m not dealing with this again!”

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Yeah that mention in the article is pretty dubious but is not about "depopulation" and for sure not about a definitive process. By our current knowledge we suppose there was a crisis on public urbanism in many baetican cities since late II and during III century, simultaneous to the lost of economic prevalence (almost monopolistic) that Baetica had in western part of roman Empire from Julius Caesar to Antoninus Pius (and the growth of Africa or Syria) and the frequent attacks by the african mauri specially serious since 170s. There was a crisis in Baetica from Marcus Aurelius to Diocletian, for sure, but we ignore its severity and extension and could be perfectly more a stagnation in an immensely wealthy and urbanized province that became "relatively" less prevalent, but still very urbanized and rich, than a true decline. Our knowledge is very limited though, we still ignore even the location of half of the cities in Baetica mentioned by literary sources or epigraphy, over 100 lost or dubious roman cities (most of them probably under unidentified current andalusian towns, more than ruins in the countryside).

To put things in perspective: During all roman period Baetica had triple number of cities than Britannia, in a smaller area. It was the most urbanized "big" region in the western part of the Roman Empire during I and II centuries with the only exception of central Italy. Its economic relevance was so huge that altered the landscape of Rome itself with the creation of Monte Testaccio, created with millions amphorae, vast majority of which came from Baetica. Despite the relative crisis during III century, it seems that Baetica recovered at last decades of that century and remained relatively relevant, wealthy and very urbanized in mediterranean or european contexts until the next splendorous period started: Al-Andalus.

We know that Al-Andalus urbanism was incomparable to any place in Europe. Caliphal Kurtuba was one of the largest cities in the world during IX and X centuries while taifa and Almohad Seville was the second biggest city in Europe during XI and XII centuries after Costantinople, but besides those big cities other hundreds smaller urban centres flourished across southern Iberia and while the great metropolis were matched in some few places, the constellation of minor cities of Al-Andalus and the urbanization rate hardly repeated in any other "big" zone of the world during IX-XIII centuries. Later, despite a relative decline, christian Andalusia remained as the most urbanized place in Europe until XVIII century. At 1600 when Netherlands, the leader among independent countries had only 24% of its population of 1.4 million living in cities over 10,000 inhabitants (19% in Italy, 10-15% in most Iberia, 6% in England), Andalusia with a very similar population than Netherlands had over half, close to 60% living in cities over 10,000 inhabitants.

Even ignoring the detailed evolution of Baetica urbanism from III to VII centuries, it seems highly unlikely that one of the most urbanized places in the roman world at early II century became suddenly deeply "depopulated" and urban centres "crumbled" for centuries, but just to increase again as one of the most urbanized zones in the world during Medieval and Early Modern periods. It's pretty obvious to me that the crisis, if existed, was relative, short and not really deep, allowing the recovery and growth of southern iberian urbanism in the next centuries.

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It was a risk province. There are reports of berber (mauri) raiders that Breached through the defenses at mauretania tingitana and raid the province in the 3rd century as Well as frankish pirates raiding its coasts

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