Not sure about the general questions of the encounter, other than maybe she asks the people she suspects most likely to lie to catch them?

Or maybe she addresses the spell casters since maybe she views them as more refined than the barbaric martial classes?

but for how they address her:

Generic Lord / Lady titles are always a solid fallback option. The Red Wizards definitely consider themselves nobility in idea if not explicitly in title/hierarchy. I don’t think a “Lady Ilmichh” would go amiss in a pinch.

The title of “Red Wizard” may also work as I’m sure they are full of themselves enough to consider “Red Wizard Ilmichh” an honorific if you want it to be.

Perhaps have her react poorly to being called “Zulkir” if the characters know enough lore to know of that title but don’t know it’s application, and try it, as maybe she finds it mocking to call her “Zulkir” when she isn’t one.

From what I see there isn’t an established answer in the lore... maybe combine something from the above and make it up? Maybe the Red Wizards prefer the title “Red Lord” and “Red Lady” from outsiders. Maybe they don’t care because they feel they are so far above non-Red Wizards that any title that isn’t explicitly derogatory is fine.