...   Is the black staff her walking stick?

That is the general presumption hereabouts, yes.

... Rufus...

errrr... Rudolph?

I'm pretty sure Jim has stated that Mister is just a cat (the Malk theory has come up before, including (I think) during some sort of Q&A or AMA).

Obviously, Jim could have been lying... or can just change his mind.
 

I wasn't thinking of it as a teaching role but more of police function or even a position similar to Mab's but covering magic. Harry would get a limited Intellectus to warn him of major magical threats and events and have the newly formed Wardens as enforcers and the Paranet as the administrative and education arms of his new council/court.

So far as we know, all mantles are constructs, made by an entity for a purpose.
Who could (and would!) create such a mantle?

I suppose the Archive has the knowledge to create it; and there's enough power on the Island to do the implementation... but, why would she?  Her Oblivion-War duties are big on secrecy, and adding a new & independent globe-trotting Mantle to the mix looks like a huge gaping OpSec hole...

The Gatekeeper sent Harry that cryptic "black magic in Chicago" message; so he seems to already be capable of doing "black magic scans" & the like (though  that could have just been smoke & mirrors, with Mab tipping off the Gatekeeper to feed Harry the bait, so she could reel him in...) .
 
Also, Harry "I've got Authority Issues" Dresden would himself be a really ironic target for becoming the ultimate Authority Figure on the issue of Magic!  (this is not, I should note, any argument that Jim wouldn't inflict such a thing upon Harry!)

I think what's particularly interesting to consider is how long Harry will live, and how much will we see of his whole existence. Wizards live several hundred years, and give this story goes into the End of Days and is titled "The Dresden Files" one might assume we see his whole story. Jim has openly said in previous interviews that he isn't sure if Harry will survive the series.

Dresden may indeed die at the end of the BAT; it seems entirely possible, maybe even probable.  But I'll note that the series is also called "The Casefiles of Harry Dresden," so if he moves fully into the "Wizard of Chicago" gig, that'd be the end of the whole PI-oriented casefiles" schtick.

... Harry may well form another White Council after the inevitable collapse of the current one. But if the White Council collapses around the various apocalypses, is there even much point? 

My notion (I think it's one others share) is that Harry leverages the Paranet to build a broader coalition, one not exclusive to "White Council Caliber" talents.  The foundation IMHO would be educational:  "how not to fall afoul of Black Magic ways."  This, above all -- the lack of WC guidance for the proto-wizards who fall (all too easily) into the lures of power -- is the thing where Harry feels most-keenly that the WC is just not doing a good-enough job.  And the Paranet is well-suited (in terms of "feet on the ground" & connections into communities) to spot these cases and intervene before things get to the "call for the Grey Cloaks" stage.

It doesn't even have to wait for the WC to collapse -- it could start right away, using the Paranet to begin educating Paranet-level talents.  And if they occasionally don't report every single "Wizard Caliber" talent up the tree to the White Council...  Well.  That just adds more complication to Harry's life (which after all is Jim's bread&butter (and mortgage)).

... Not only that, I think it should be noted that Harry fundamentally rejects authority. While he has matured and become less abrasive, he ultimately still dislikes the idea of any governing body being in charge of him or anyone else. He's quite the libertarian. So, in the event the White Council does dissolve, I don't know that Harry would be the one to rebuild it. That's more of a Carlos type-of-thing ...

As others have said, it's not really anti-authority.  It's anti-bullying, and anti abuse-of-power.

But earned expertise and good judgement -- being an authority, not just having a position of authority -- is something Harry respects, and often yields to.

... do we know when the white council was actually created? I can't remember any hard evidence other than when Edinburgh was won...

https://www.youtube.com/watch?v=ODOhEdiFwW0&t=1733s
"The origins of the WC were pretty nebulous... they were an advisory board to the Roman Senate for a long time"
But then Merlin reorganized them after the fall of Rome, for fear the powerful wizards (now ambitious independents) would war among themselves.

"for a long time" isn't terribly precise.  We don't know if they coalesced after Rome demonstrated its hegemony in the region, or were an older group that attached itself to Rome, or were part of the founding (which would firmly place them around 750BC(ish))... q.v. "nebulous."

Similarly, "fall of Rome" is pretty indeterminate... a long slide from about 375AD to 475AD; so there's at least a century where Merlin might have reorganized the old Roman group into the new White Council (and whether that took just a year or two, or decades, or even a century... also unclear).

No idea if this is something Jim just hasn't decided, or if he's intentionally obscuring something (for a later Big Reveal), or what.

It's possible on Merlin, but if you go by mythology, Merlin had long been asleep by that time. 

But Merlin was a wibbly-wobbly, timey-wimey sort of wizard.

Just because he was sent into an enchanted sleep in the 400's-600's(ish), that doesn't mean (in his own personal back-and-forth-through-time lifespan) he hadn't already marched with William, and visited other future times as well (possibly even to the yet-unwritten future of the DF timeline).

Before-and-after, for Merlin, is virtually impossible to determine from our information.

I understand, but if you go back and read the different definitions of what an unreliable narrator is, Harry really doesn't fit, at least not consistently ...

The naive (aka ignorant) POV is one of the key types of "unreliable narrator."

And Harry is always ignorant.

He starts that way (q.v. Jim writing an actual, literal, "talking head" to "educate" Harry); but, despite how much he has learned, Harry stays that way:

• he's a magical heavyweight, and he's fighting his way into the deeper & murkier end of the supernatural power-pool
• he's also a PI, so he inquires & investigates as a central element of his professional life

Despite all he has learned, he keeps forging out beyond what he knows, into new areas... areas where he's still ignorant.

Again:  the books rely upon Harry's ignorance.  Even when he's not working for a "paying customer," he's usually investigating things.  This is central to the genre that Jim's writing (with the DF novels).  If Harry were to become "knowledgeable" he'd become a quest-giver minor character, instead of a questing protagonist.

Finally, I reiterate:  Jim himself says that Harry is an unreliable narrator.  When professional writer (who has not only a bunch of successful novels, but a bunch of academic & workshop training in writing) says "I used this well-known method" ... I honestly don't understand why it's so important to you to deny it.

... Too many times the term "unreliable narrator" is the fall back crutch when there is no evidence to prove the poster's point one way or another ...

OK, this is an entirely different point!  And it can be a crutch, yes; but equally, it can be simply point out that just because Harry says such-and-such is "true" (like his early reports of Mab being "the archetypal evil queen"), that too isn't really "evidence" that "such-and-such" is a "truth" of the Dresdenverse.

Harry can tell us 100% "the truth as he understands it," and simultaneously Jim can be 100% lying (without even that Faerie veneer of "technically true, but you misunderstood").  Harry is just wrong, very very often.