I'd like to see some Headquarters be that BFS, Mab's or Vadderung's WarRoom have Little Chicago as a centerpiece.

Hmmmm, I just thought of an issue with TTHarry acting in PG.  It's a little vague and probably workaroundable but it is a genuine issue that is new.

In PG Slate still holds the Winter Knight mantle.  If TTHarry is still the Winter Knight when he is doing his alleged shenanigans in PG, wouldn't the dual mantle presence present its own paradox?

Actually, I encountered this same conundrum when I predicted a (Kumori=Maggie Sr) and (Kumori/Maggie Sr has Lasciel's coin) theory.  A reality with time travel could have multiple coins of the same Fallen existing at the same point in time, particularly if they are carried there by a time traveler.

But this same problem exists when one has the same individual present multiple times within same timeframe.  There are probably similar mechanisms that explain both.  TTHarry (from future) would be pulling power from the FutureQueens not from the current Queens.  Future Queens determined that it was necessary to defeat a gambit in the past by sending their knight and power into the past, it weakens them in their current time but its likely that the enemy did the same thing by sending their power into the past which then required a response from the Queens.

It seems to me that it is Mother Summer and Winter that have jurisdiction over of matters of time.  Like there is a distribution of responsibility for each level in the Queens hierarchy.
Time;                                       Time
Winter and Outergate;               Summer and Mab;
Winter and Mortal Realm            Summer and Mortal Realm

WHY MOLLY?

This is difficult to guess, and can seemingly only be explained by assuming Maeve knows more than she should. Either Maeve knows that Molly is Harry's best friend's daughter and a mortal practitioner coming into her talent, or it is an amazing coincidence that her plan hinges on. We know Arctis Tor was attacked by a rogue Denarian. We suspect this rogue Denarian was a Nemesis agent with a Coin. It's plausible to posit that Maeve and Nemesis sent another agent, the rogue Denarian, to clear out Arctis Tor, leaving the Wellspring unguarded why Mab was curing the Leanansidhe. And through Lea and the Denarian, it's possible Nemesis knows about Michael. But what about his family?

Gregor. Molly was targeted as Charity's daughter, and not as Michael's. We know she has Fae in her ancestry, and that this is likely the source of her and her daughter's talents. I posit that Charity is Aurora's descendant. Future Harry, by the way, isn't the only player operating on the periphery. Someone else is in town.

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The sun had risen on our way there, though heavy cloud cover and grumbling thunder promised unusually bad weather for so early in the day. That shouldn't have surprised me either. When the Queens of Faerie were moving around backstage, the weather quite often seemed to reflect their presence.

We see this again in Small Favor and Ghost Story, where particularly frigid weather means that Mab is in the area. So, let's check out the opening to Proven Guilty's second chapter:

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I turned my back on them and walked out of the warehouse into Chicago's best impression of Miami. July in the Midwest is rarely less than sultry, but this year had been especially intense when it came to summer heat, and it had rained frequently.

What the hell is Titania doing in Chicago? Combining this with Mab's assertion that Molly would be a better fit for Summer and the symmetry of a Winter scion becoming the Summer Lady while a Summer scion becomes the Winter Lady, and it's not unreasonable to conclude that Molly's Fae ancestry stretches to Titania.

But that doesn't answer what Titania's goal is. Fix and Lily aren't working towards it. They're working towards Maeve's goals. It would be a stretch for Titania to be infected with Nemesis, wouldn't it?

I suspect that Titania was trying to groom Molly to be Lily's successor, subtly, in the background. Maybe by nudging the right books into Molly's hands. I suspect that Winter's Queens knew this and were keeping tabs on Molly for that reason. And when the pump was primed, Maeve chose Molly to use as a fear anchor.

This is the wildest-assed guess, but I think it holds up

To me, the above quoted piece is pioneering work that I haven't seen before on this forum.  The plausible link between Titania and Titania's choice for Summer Lady being that of Molly is excellent.

There's another time traveler in the tale, and I suspect he's working with Thomas. It seems suspicious that Thomas is tailing Harry on this one adventure. But there's something I noticed once Thomas joins the plot: he does his best to remain uninvolved.

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I glanced at Thomas, who was facing away, a little apart from the rest of us, staying out of the decision-making process.

There are other instances where Thomas basically wallflowers. He's very careful not to disrupt the natural flow of the case as much as he can help it. I think, like Rashid, Thomas has future information.**

Hitting Harry keeps him out of the apartment. I posit that Future Harry is at the periphery in Proven Guilty, and whenever Harry is out of the apartment, Future Harry is using it as his base of operations. Future Harry has Thomas as a knowing accomplice.***

This is another strong argument that Thomas knows more than he lets on.  Prior theories had interactions between Thomas and LC Fixer, even a time traveling Harry, but it seemed that no theory suggested that they were closely working together. 
When Harry comes home and finds Thomas all packed up and ready to leave, there is a strange conversation between Thomas and Harry.  About Mac's brew frozen into ice cubes, that Thomas says Mac would kill you for freezing it, that Harry says Mac can come over here and... (forget the final bit of the conversation).  But there seems something that Thomas is trying to tell Harry, some hint about upcoming events.  One could argue its simply chatter leading up to Thomas telling Harry that he is leaving though I'm sure Harry already knows that considering the packed bags.

Not to detract from your accomplishment but to state fact, the hot weather had been pointed out previously and it had been linked to Titania but no theory went any further than that.   No one that I saw ever attempted to link Molly to Titania, Titania's play in PG, and Mab's statement in Cold Days, even viewed with hindsight.

I'm more of the mind now that Proven Guilty had Titania all over it.

Titania is assisting Mab by constraining Lily's options and outflanking her when needed.  I'm now wondering if perhaps Titania fixed Little Chicago, if Sandra was an agent of Summer, Titania was aware of an assault on WInter and acted to take up some of Mab's duties.  It's not required though that Titania be the one who fixed Little Chicago.

Now, why would she do that.  Well, in the Disprove the Duck thread, I asked myself if Molly=Mab who traveled into the past, and Mab has a biological sister, then wouldn't Titania be one of Molly's sisters.  If true, she definitely would have an interest in preserving Molly's future and preventing any gambit against Molly/Mab that would greatly change or skew Mab's current identity.  This though would seem to suggest that the Queens know who they are, and can predict from this fact a great many things, particularly those of great import that must be done within the timeline.  Those acting against Molly and Sister are acting against Mab and Titania.  The opposition is trying to destroy this reality by changing Molly's or her Sister's, or both, future and consequently past.

This reasoning would be equally valid if Molly simply was Summer's choice for a new Summer Lady.  Titania wasn't pleased with Lily and she began acting to address this deficiency. 

Now consider, all attempts against the Carpenter's family whether that be Charity, in the case of Gregor, Nightmare, and Scarecrow, or Molly in the case of Artur Langtry, Convention Set Up, Capiocorpus, attacks on Molly during Ghost Story etc, kidnapping of Alicia by

Dead Beat
- Incidental observation that feels like it fits in with this model somehow; one thing DB accomplished was to show Harry that necromancy is not inherently evil (Kumori saving the life of random gangster dude) and then give him experience of using it himself in a not inherently evil manner (Sue). One more blade to the Swiss Army chainsaw as needed.

It does seem like cowl and kumori were working from a time travel angle or at least information about the future that guided their purposes in Dead Beat.  It seems very important to Harry's acceptance of necromancy that he was exposed to it via Kumori, and found it to be possibly neutral and/or bent toward positive aims.  I also think mavra was playing a game of pointing Harry  at the other Necromancers.  I really do believe she is a 'good' bad guy that is working against the Outsiders.  I realize her magic is Outsiderish but it would be more interesting if the black court were refugees from the Outside.  It is apparent that the Black Court requires the existence of humanity to keep their 'species' going.  I also wonder at Marcones and Gards involvement in giving Harry information that led to him getting significant information of the Necromancy that Kumori was involved in.  I also would like to point out that the ambulance driver/medic appeared in Cold Days when I believe they arrived at Molly's apartment to care for the wounded.  I believe that was Eyes girlfriend that went with them.  It is apparent that the medic will play an important part in the future.  I wonder at Kumori's awareness of this fact.  Neuro, you did a good job coming up with this referential theory.

The White Council and the Laws of Magic are mainly about restraining wizards from misusing magic and protecting the mortal world from their predations when it involves black magic.  The mortal world has its own Laws with respect to how mortals behave.  I would assume that the White Council allows the mortal authorities to deal with illegal nonmagical acts by wizards.  WC would only step in if their were violations of the magical laws.  Though their are flaws with this setup, I do see the need for the council to constrain such actions.

Aurora was killed at a special conjunction, wasn't she? That's why she was vulnerable.

When the Queens bring out the Stone Table, everyone becomes vulnerable including the Queens.
What we didn't see in Summer Knight that we did see in Cold Days is the actual mantle jumping from Aurora to Lily, or in the case of CD from Lily to Sarissa.