Who is "she" Murphy or Mab?
. Read pages 26 through 30 of Skin Game, Murphy gives Harry the big lecture about isolating himself from his friends...  Her attitude is that Harry purposely did that, and she is worried about him.. If she knew the skinny, she wouldn't have given the lecture..
Apparently he didn't lay anything out and Murphy didn't ask, again read pages 26 -30..  A] No, it appears that Harry didn't mention Mab.. B] From the text, no, Murphy didn't ask, she assumed some psychological explanation about Harry isolating himself on the island from his friends and family on purpose..  It may not be a lack of caring, but it is idiotic amateur psychologist at work.. C] Bingo, if she truly trusted him to have his secrets... Then she'd truly trust him to have a good reason for those secrets, ergo not give him shit in the form of a guilt trip about his friends being so concerned because he purposely isolated himself on Demonreach for a year...  Just a "missed you Harry what's the plan?" Would do  nicely.if she truly trusted him...

Sorry, but I don't read it that way.  Can you quote me the exact text you are referring too.  However, before you do so, this is what I found:

“You could live here,” she said. Then added, a beat too quickly, “In Chicago. You could, you know. Move back to town.”

I frowned, still playing with my cat. “I don’t . . . Look, when the next freak burns down my place, maybe I won’t get as lucky as I did last time.”

“Last time you wound up with a broken back and working for a monster,” Karrin said.

“Exactly,” I said. “And it was only because of literal divine intervention that none of my neighbors died.” I shook my head. “The island isn’t a kind place, but no one is going to come looking for trouble there.”

“Except you,” she said gently. “I worry about what will happen to you if you stay out there alone too long. That kind of isolation isn’t good for you, Harry.”

“It’s necessary,” I said. “It’s safer for me. It’s safer for everyone around me.”

The dialog continues and Murphy speculates why Harry is afraid to move back to Chicago, but clearly they are talking about the future and not talking about why Harry had already spent so much time on the island.  More to the point if you go back to the very end of Cold Days you will find this bit of dialog in a short discussion between Thomas and Harry as Thomas and Murphy are about to depart:

"... That thing the island said was in your head?"

"Another reason to stay here," I said. "If Molly's the one who can help me, I'm on my own for now. But Demonreach seems to be able to make it leave me alone, at least while I'm here. Pretty much means I need to stay until Molly gets herself back together."

Even if you assume Murphy was on deck and didn't hear the conversation; which seems somewhat unlikely to me, you would have to assume Thomas never told Murphy about why Harry decided to stay.

I'm in agreement with you about Murphy's reaction to Harry in Cold Days.  She is somewhat cold and her first words are definitely accusatory.  "I hear you belong to Mab now."  I just don't see that attitude carrying over to Skin Game. 

Now the swords are a separate matter.  I don't think Murphy was wrong to keep the swords in her possession in Cold Days, however that doesn't mean she was right to assume she would remain their custodian in the future or that she would know when the right time had come to use them. 

However, even the swords are a secondary matter in the greater consideration of Karrin Murphy's personality.  She was definitely damaged goods in Cold Days.  Butters could see that and told Harry.  Also, it seems to me that when Murphy tried to analyze Harry in Cold Days she was projecting her own situation and fears of where she was headed, into Harry's situation.  (Relevant Quote below.)  I think this is true even if some of her analysis was correct.  I don't think she was the same judgmental person in Skin Game and despite the debacle with the sword she appeared to be getting better.  Now that could all change in Peace Talks, but we will have to wait and see.   

"I'm not angry at you, Harry," she said. "I don't hate you. I don't think you've gone bad. A lot of people have fallen into the trap you did. People better than either of us."

"Uh," I said. "The evil-Queen-of-Faerie trap?"

"Christ, Harry," Murphy said quietly. "No one just starts giggling and wearing black and signs up to become a villainous monster. How the hell do you think it happens?" She shook her head, her eyes pained. "It happens to people. Just people. They make questionable choices, for what might be very good reasons. They make choice after choice, and none of them is slaughtering roomfuls of saints, or murdering hundreds of baby seals, or rubber-room irrational. But it adds up. And then one day they look around and realize that they're so far over the line that they can't remember where it was."

...Dammit Mab. She's been known to do that for the right reasons despite potential consequences, when she hung Slate up to cool off.

If Mab has the coin my guess is that she can't hold it forever.  It would be like a football team deciding to play in a basketball league or put it this way, Mab is out of her jurisdiction if she thinks she can hold the coin forever.  She has a score to settle with Thorned Namshiel and any other Denarians who worked with him to attack Arctis Tor, but I'd bet she's limited in what she can extract as retribution.   

She also had good reason to believe he was dead in Ghost Story, so why weren't her first words to Harry, "HARRY!  YOU'RE ALIVE! I thought you were dead, what happened?"

That was weird, wasn't it?  Molly was the only one who knew Harry wasn't dead.  Andi was right to wonder if she was dealing with Harry or an impostor.  Thomas' reaction; his anger, was entirely believable.  Murphy said she heard about explosions.  Actually these are her exact words:
Harry -  "Yeah," I said. "How'd you find me?"
Karrin - "Scanner. The last time a bomb went off in this town, it was in your office building. I hear another one goes off in the street, and then reports of explosions and gunfire out over the lake just after dawn this morning. Math wasn't hard to do."

Seriously?  With the Fomor, the White Court and Marcone all staking a claim to the city those noises could have signified battles between any two or all three of those parties.  I think a more believable reaction might have been if Murphy had mentioned the bomb, explosions and gunfire and said that she "hoped that only Harry Dresden could be at the heart of such chaos." 

There was one other thing missing from Karrin Murphy's reaction to seeing Harry alive again.  Karrin Murphy didn't say, "I'm glad your back" or "I'm glad your alive Harry."  Even with her concerns about what Mab might have done to him, you'd think Murphy might have expressed some positive emotion at seeing Harry in the flesh again.  Instead she went straight to the accusations.   

Actually, now that I think about it, Butters reaction to a living, breathing Harry was also a bit strange.  You'd think that after talking to someone's ghost you would want to know how they got their body back.  In Butters defense it could be argued that he was preoccupied sewing up Harry's wounds at the time, but I'm surprised that Butters; or anyone else for that matter, didn't press Harry for any details about his out of body experiences.  Granted Harry's response couldn't have gone much farther than, "I don't have time to explain it all now, if we survive the next twenty-four hours you can ask all the questions you want and I'll answer as best I can," or something like that.

I feel like there is an entire conversation; or maybe two, missing from Cold Days that Jim either decided not to write or did write and decided to scrap or drastically shorten. 

There's something really odd thing about the attack on Arctis Tor.

* Mab moves the bulk of her forces to the border with Summer, which pins Summer's forces in place to defend against a possible incursion from Winter which prevents Summer from retaliating against the Red Court for it's incursion into Faerie. (I'll get back to Mab later.)

* The Black Council appears to be in league with Outsiders.

* Somebody called up Outsiders to help the Red Court in it's battle with the White Council.  Presumably these rogue wizards are members of the Black Council or at least it's magical foot soldiers.

* Nemfected Maeve works to gain Lily's trust.  She helps Lily carry out a plan which allows Summer to strike a blow against the Red Court.  This plan come to fruition because of Harry's assault on Arctis Tor to rescue Molly.

* The Black Council attack on Arctis Tor preceded Harry's rescue mission and even though it killed off Mab's troll bodyguard, overall that attack failed.

I don't think the Black Council attack was an attempt to free Nemfected Lea or to take out Mab.  I don't think one denarian; even their best magic user, was enough to threaten Mab in her stronghold.  (I'm assuming Thorned Namshiel had help, but he was the strongest player on the enemy team.)  I think the attack was an attempt to do what Lily and Maeve later succeeded in doing, allow Summer to attack the Red Court.  Specifically, I think they wanted Mab to recall her forces from the border with Summer so the Seelie Court could attack the Reds.  I think the Black Council decided to nerf to Red Court so the war could drag on, and this would slowly degrade both the Reds and the White Council.  I don't think they wanted either side to have any easy victory.  Remember that in Dead Beat the White Council was in pretty bad shape.  I suspect the Black Council and it's Outsider (allies? overlords?) buddies saw the Red Court much as Nicodemus did, "They're parasites who are inconvenient in the short term, dangerous in the middle distance, and fatal to any long-range plan."

The alternative is say that Nemfected Maeve was willing to allow Lily and the Summer Court to have their moment and help the White Council in it's war with the Reds, all so Maeve could completely gain Lily's confidence so that one day Maeve could bring about the downfall of both Summer and Winter.  I suppose that's possible, but then it leaves the Black Council attack on Arctis Tor unexplained unless you really believe the BC thought they could storm Arctis Tor, which I find implausible.  However, either explanation; my nerf the Red Court or Maeve's palace intrigue hypothesis, tells us the Black Council had no problem stabbing the Red Court in the back when it suited them.  One more thing to consider is that nerfing the Red Court and helping Maeve worm her way into Lily confidence could have become duel goals to be carried out simultaneously.  It could have went down this way; the Black Council attack fails to get Mab to draw her forces back from the border so a new and improved plan succeeds and helps nemfected Maeve at same time.   

Just to make things more difficult to comprehend, there's a question no one seems to be asking and one that really needs to be answered in order to understand what actually happened.  Why did Mab order her forces to the border with Summer in the first place?  I used to think Mab made a deal not to attack the Red Court and help prevent Summer from doing so, but if this was the case, why did Maeve make it possible for Summer to attack the Reds?  Do you see the contradiction here?  Jim has been holding out some vital information which would allow us to untangle this puzzle.

P.S. You know, there's another explanation for why nemfected Maeve was willing to help Lily, but right now I'm too tired to type it out at the moment.  I'll do it tomorrow.

While I agree with the main point of the OP that Murphy's ability to be in the thick of the fight has been severely diminished and it may seem that she could become redundant to the overall story; however, I think Karrin Murphy helps keep Harry's perspective and perhaps his morality anchored in the real world.  Without her he might as well take up residence at Arctis Tor (OK I'm ignoring his daughter for this hypothetical example) and only come out when someone sets off a BAT signal that Chicago needs help or Mab needs something done or done in. 

I'm not saying I like everything Jim has done with Murphy since Changes; particularly in Cold Days, but at the end of the day I think she's in the overall story arc for more than her physical toughness.  A perfect example is Murphy in Summer Knight when Harry finally spills his guts and tells her about the White Council or in a later story when Harry tells Murphy that he's afraid he might really be the ticking time bomb the Council thinks he is.  Karrin Murphy is more than Harry's cheerleader in these situations and she does more than just give him good advice. (Well most of the time it's good advice.)  She keeps Harry centered in a way that no one else does.  I'm not sure how to express it more clearly than that. 

If Murphy was to die anytime soon I think it would be hard for Harry to remain himself.  He would necessarily become a darker character.  I think that would be the case even if he managed to become a decent father.  Harry has already had to face his darker impulses that Lash brought to the surface and he continues to battle Winter's influence.  Let's not forget that Harry had to kill Susan to save his daughter's life and the lives of his friends.  I not sure I would want to read him any longer if he has to take another blow like that. 

Finally, even if she came back as a Valkyrie I doubt Karrin Murphy could be same moral force in Harry's life that she has been before.  Without knowing how Jim would write such a transformation I am willing to bet it dramatically changes the perspective and eventually the personality of the person involved.  It wouldn't be the win-win scenario some people think it would.  Now that's just speculation on my part so I'll leave it at that.

The WOJ was ambiguous to an extent, but given that his phrasing was 'fast ally' I think prevailing opinion was that she's an ally to evil Mirror Dresden. Prime Harry might collaborate with her temporarily if it was necessary to confront a mutual enemy he considered even worse, but I don't think he could condone her as more than a temporary truce of necessity.

What Mavra can't tell the difference between the two Harry's?  Prime Harry could work with Mavra, but for a different goal than what Mavra would expect. 

Oh, Donald had tons of integrity left by the early books.  Intolerant, yes.  An ass, oh yes.  But integrity out the wazoo.  He just directed it badly because he was more or less a burn out after a century of fighting dirty wars and monsters.

Yes to this, and Morgan is (as best I can recall) supposed to a little over 100 when the series starts.  He fought in the First World War.  So Morgan becomes Luccio's apprentice something like 30 - 35 years after the events in Fist Full of Warlocks.  That's plenty of time for her attitudes about life to have hardened and for her to believe in the need to encourage toughness (for lack of a better term) in those she would train to follow her.  Not that Luccio isn't strong in this story but she is definitely in transition to the Luccio we meet in Dead Beat.