The guy with the cursed sword was already being manipulated by the demon at that point, but still he was only there to make an excuse so the MC and Beatrice can get closer, and to explain for what are those cristals around the map, if you didn't explore. I don't know if a similar guy appears for the other queens.
To be honest I didn't get that ntr scene with Beatrice and the Baroque in my first run so I can't judge well that. In my opinion the game is more focused around the relation between Seria and the MC, since she's the only one that gets "choices" when you speak with her, also the game trolls you with her in this choices, if you pick the ones that you think will make you closer to that charater, the game will always trigger the ntr scene with Baroque and her and it also feels the same as you describe the scene with Beatrice. But I don't know what else could they do against the King's order since it is a ntr focused game and the MC is a dumb dense guy, one of the cliche type of characters that get ntr. But in that regard now i get you, I did also complain about something similar in the thread of the game Alansya Chronicles: Fleeting Iris, where the FMC loves her fiance very much that she even moves from "Japan" to "The USA" where he lives, but in almost every route you pick she goes from 0 (pure) to 100 (slut) as soon as she watches a big D or gets blackmailed (she can counter the blackmail very easily or at least make her corruption more difficult, her fiance is a CIA agent) so to me it was also illogical and unsatisfying (in some routes). And I tried to summarized it by saying she was too weak mentally, and people were like "no she doesn't have a mentality, she is a slut 'cause you make her that way duh" and I was like, I never complain about that, I complain about the process that makes not sence but I got the same answer. So I guess we shouldn't expect something logical or complex in this kind of ploty ntr games.
The princess from the desert kingdom is Carla, that kingdom is SE from Diamond City, but you can't pick that kingdom to start with. The knight's kingdom at the West is Leane's, and the kingdom of the Priest Queen is SW from DiamondCity, Marion is a noble that (if you pick that faction) is always trying to keep you away from the Priest Queen, like Wendy. But I wouldn't complain about them not getting any notable scene if you didn't pick 'em at the start since the MC isn't meant to have a harem and to me,it makes sense that if you want to know more about them, you need to pick their faction from the start.