You’ve complained about the world of ice and fire saying that the field of fire army of the reach and west was too small to be the largest army of westeros and seem to treat canon times kingdoms’ army and population size as being the same going back centuries or more, but doesnt that ignore population growth? It could well be the case that the field of fire army was the largest because the population of westeros was much lower in the past.

Premodern population growth is extremely tricky to generalize about, because you have some rather significant changes from period to period:

  • Late Antiquity (200-600 CE) saw significant (almost 30%) declines in population, due to repeated plagues, the collapse of the Western Roman Empire and attendant wars and decline of trade, and a decrease in global temperatures that reduced crop yields. 
  • Early Middle Ages (600-1000 CE) was pretty stagnant in terms of population growth. More plagues, dislocation due to various invasions, low levels of productivity, etc. 
  • High Middle Ages (1000-1250 CE) saw a huge population boom. Huge areas of wilderness were cleared and cultivated, the climate got warmer which meant that growing seasons got longer, relative political stability made new settlements less risky, trade expanded and with it so did urbanization, etc.  
  • Late Middle Ages (1250-1470) saw significant declines in population during the crises of the 14th century, including both the Great Famine of 1315-1317 and the Black Death (which all on its lonesome wiped out about 50% of the population of Europe). 

But beyond that, we don’t see evidence of significant Westerosi population growth in recent years. King’s Landing isn’t noticeably bigger in population in 300 AC than it was in 26 AC when the walls were completed; Oldtown’s population doesn’t seem to have changed either in that period. The North’s armies stood at 30,000 strong at the time of the Conquest; they’re not noticeably bigger now. 

Finally, part of the problem of attributing the difference to population growth is that you have to explain the sudden shift in growth rates in the last 300 years vs. the previous 8,000+ years. 

Why does Stannis leave Melisandre behind at Castle Black? They both agree that he could have won at the Blackwater if she had been with him and in the show she even warns him about making this mistake twice. So why in the books does she stay behind? Was it to watch over Mance? Or maybe to see if she could seduce Jon?

I’m pretty sure that Stannis leaves Melisandre at the Wall because that’s where the real threat – the White Walkers – is coming from. In his eyes, the fight against the Boltons is a mere shaping operation intended to unite the North so that he can redirect its resources to the war against the Great Other. 

Does house Arryn have a look like the lannisters, starks, baratheons, and tullys do?

Yes. We know this from when Sansa meets Harry the Heir:

Ser Harrold Hardyng looked every inch a lord-in-waiting; clean-limbed and handsome, straight as a lance, hard with muscle. Men old enough to have known Jon Arryn in his youth said Ser Harrold had his look, she knew. He had a mop of sandy blond hair, pale blue eyes, an aquiline nose. Joffrey was comely too, though, she reminded herself. A comely monster, that’s what he was. Little Lord Tyrion was kinder, twisted though he was.

Blond hair and blue eyes attest to the Arryns’ Andal heritage, but the aquiline nose I think is the more specific detail, evoking the curved beak of the falcon which the Arryns took for their sigil. 

Do you think a partition of the Riverlands might have enabled the Kings of the Reach, Rock, Vale, etc, to bring their portions into a more stable state and improve their prosperity? Alternatively, without even a weak sovereign or national identity, would the partioned Riverlands simply have become a permanent battleground like the Disputed Lands in Essos, as those hegemonic states fought over each others’ riverine possessions?

More the latter. The partition of Poland didn’t work out very well for the Poles, nor did it stop the Prussians, Austrians, and Russians from fighting each other over Poland. 

Would powerful nobles have their own courts at their personal castles, like the hightowers or redwynes or reynes would probably, but what about rowans or royces or brackens and blackwoods? what would those be like?

Absolutely. Indeed, we’ve seen examples of much smaller lords with their own courts: think about Lady Rohanne Webber, who has Septon Sefton and three septas, Maester Cerrick, Ser Lucas Inchfield her castellan, Lady Hellicent Uffering her former goodsister, a dozen knights and squires, and various pages. That’s a pretty significant household for a minor noble house. 

So for lords of the Rowans or Royces or Brackens or Blackwoods, imagine that but scaled up – add on the relatives of their vassals who might serve as pages, squires, castellans, masters-of-arms, stewards, ladies-in-waiting, add on the households of other noble families who’d married into the family (except much larger households than the occasional septon or unmarried sister, because one of the ways you demonstrate how awesome you are is to have a bigger retinue than anyone else), and so on and so forth.