@shylarah"I'm not surprised about the ladies being taken. I am surprised about the kids. I mean, why would Varya want royal kids of other nations? The houses aren't still in power, so it doesn't really legitimize Varyan rule (and I'm not sure that it would to start with). The kids are kept there, so they're (probably) not being raised as loyal Varyans -- that'd be more effective by putting them in a family. So why deliberately breed royal kids? It seems like this'd cause Varya more trouble in the long run."
The Scarlet House is both a brothel and a strange sort of exotic sperm bank. It's not an official part of the Varyan government and it isn't meant to be a place that produces legitimate heirs, but instead it gives nobles and clergymen the opportunity to sire children who have blood that can be traced to royalty (which is, in itself, a largely Varyan fetish, since theirs was a nation that answered directly to their God, and didn't have an intermediary royal family of sorts). So all in all it's meant to be a fucked up fetishistic/exoticism thing. Imagine a place where horribly rich Americans can pay to be Meghan Markle, all while their version of Prince Harry was a genetic slave. There's also the "high class pleasure house" aspect of it, which is just, yeah.
Rose, Fie and Vahn were meant to be breeding material. Unlike them, most of the children born there are taken to live with their noble parents as like, third-born bastards (they're pretty much "trophy kids"), while those sired by members of the clergy are brought up in the Church directly as sort of "sponsored" individuals. Magnus was one of these kids.
As for Warband Ifrit, I'll just say that it's one of the old warbands who's designation isn't used anymore. Our characters wouldn't know about it, but if they wanted, they could readily find out more by asking around. I'll also say that yes, the name was intentional.
EDIT: Oh and as for High Inquisitors, they're pretty much military generals. I've also added the Inquisition Hierarchy to the First Post.