I'm working this one out, based on Bayonetta.  There would be a parallel form for Lumen Sages, as well, though there may be a few changes in between the two.  I'm not sure of the power level though.

Umbran Magic
Description: Being bound to a demonic power of Inferno, the Umbra Witch is capable of summoning demons and slowing subjective time in combat
Agenda: Destroy the angels of Paradiso (up to the GM if this means the actual angels of the Dresdenverse or a separate form of Nevernever spirit, akin to the difference between a Fallen and the frog demon).
Evocation: Umbra Witches are able to use Chronomancy to a limited extent; they cannot travel through time, but are able to slow it down when threatened.  They also are able to use their Hair as an element of magic, akin to Air or Spirit in function.
Thaumaturgy: Demon Summoning
Evothaum: Umbra Witches can use summoning magic and alchemy with the speed and methods of evocation (for the latter, this still requires ingredients and appropriate recipes).
Extra Benefits: 

Any suggestions or alterations welcome!

Actually, Nathan as Harry fills in the gap in my own dreamcast of the series.

Here are some of my other roles:

Bob: Alan Rickman (Can you imagine him saying “And they have boobs?”)
Nicodemus: Robert Downey, Jr.
Gard: Jaimie Alexander
Donar Vadderung: Jeff Bridges
Arthur Langtry, The Merlin: Geoffery Rush
Ebenezer McCoy, The Blackstaff: Donald Sutherland
Ferrovax: Ralph Fiennes
Rashid, the Gatekeeper: Idris Elba
Lea: Eva Green
Mab: Alex Kingston
Maeve: Natalie Portman
Titania: Nicole Kidman
Lily: Emily Browning
Aurora: Kiera Knightly
Erlking: David Bowie
Kincaid: Tom Welling
Uriel: Don Cheadle in "Small Favor;" Tom Felton in his blond aspect

To go back to the original question for a moment, I think that, as has been said, the duties vary for the different queens.  However, a few things seem to make sense:
-The Knight acts as a bodyguard for the Lady when she needs one (possibly whenever she ventures into the mortal world).  We didn't see Slate with Maeve in PG because he was... not free to leave.  But after SK, we NEVER saw Lily without Fix (though we did once see the inverse).  Since the Lady is about as strong as a really powerful wizard, it's possible that the power of the Knight is placed with her more than with either of the other Queens (based on what we've seen and what Jim has said, NEITHER woman needs much in the way of bodyguards, even away from their centers of power).
-The Knight can be sent on mundane tasks.  Generally they won't be wasted on things like coffee fetching (unless it's a "If you're going there, can you get me one?"), but retrieval of items seems to be on the list.
-It's not outright stated, but thus far only the Queen seems to be able to ORDER a kill.  In SK, Maeve asked Slate to presumable for a ritual.  But why not kill her outright?  Just a theory, but maybe that's a Queen-only duty.
-Not sure what s/he does for the Mothers.  And honestly don't want to dwell on it too much...