I’m struggling with the concept that Cersei’s children would be killed if the truth of their parentage was known, particularly in the context of a society accustomed to Royal incest. Ned wanted them to live – is his objection to killing children that rare? Do the faith practise forgiveness – the children did not sin themselves-if so would they offer to take them in? On a related note, if Cersei hit her head and changed personality, would the children be equally threatened in the free cities?

The text is pretty clear on this point:

“She had seen enough of Robert Baratheon at Winterfell to know that the king did not regard Joffrey with any great warmth. If the boy was truly Jaime’s seed, Robert would have put him to death along with his mother, and few would have condemned him. Bastards were common enough, but incest was a monstrous sin to both old gods and new, and the children of such wickedness were named abominations in sept and godswood alike. The dragon kings had wed brother to sister, but they were the blood of old Valyria where such practices had been common, and like their dragons the Targaryens answered to neither gods nor men.” (emphasis mine)

Catelyn IV, ACOK

So I’d question whether Westeros is “a society accustomed to royal incest.” What they were accustomed to was treating the Targaryens as an exception to the role – although not without some sotto voce disgust (see Dunk’s reaction to Egg talking about his sisters in Sworn Sword) – and even that came after A. the Revolt of the Faithful, and B. the Targaryens marrying into other major families after the loss of the dragons, so as to reduce the frequency of incest.

Ned is positioned in AGOT as an exception to the rule – due to the traumatic loss of his family in Robert’s Rebellion and his unusual commitment to his code of honor – which we can see in the Small Council “debate” over assassinating a pregnant teenager where only he and noted idealist Barristan Selmy express a moral objection.

jedimaesteryoda asks: Septon Cellador’s antagonism towards Jon

Cellador is alongside Marsh and Yarwyck when they go to address concerns from Marsh and Co.

Septon Cellador cleared his throat. “Lord Slynt,” he said, “this boy refused to swear his vows properly in the sept, but went beyond the Wall to say his words before a heart tree. His father’s gods, he said, but they are wildling gods as well.“

Is Cellador’s opposition towards Jon based in part on being prejudiced towards those who follow the old gods or as he calls them "wildling gods”?

Absolutely.

The Westerosi seem to be both religiously conservative while also surprisingly tolerant of prostitution (brothels operate openly, pay taxes and its not even a secret that a member of the small council operates one.) Is this realistic? how freely could sex workers work in medieval/renaissance europe?

Yep, it’s pretty realistic. There’s a pretty wide literature on the history of medieval prostitution, which is very interesting if you want to know more about the history of gender, sexuality, and culture, and I haven’t read more than just the basics.

Here’s the short and simplified version: in Medieval Europe, prostitution was seen as a necessary evil, something that would prevent adultery, rape, masturbation, and sodomy (which were seen as more important sins). The Church wasn’t super happy about it, and preachers would try to persuade prostitutes to reform, but the Church wasn’t about to ban it (especially since a lot of clergymen made use of prostitutes since they weren’t allowed to get married).

What did happen is that prostitution was regulated: in some places, it could only be done outside the city walls; in other places, it was restricted to certain streets or neighborhoods; in some places, there were civic brothels that were given a monopoly on the trade.