Littlefinger knows Arya is alive. He spotted her working for Tywin.
So why is Littlefinger pointing out there are other living Stark heirs, what is in it for him? If there are other, known to the Bolton and other Stark bannermen, living Stark children that lessens Sansa’s value as the only gateway to legitimately holding the North. While Littlefinger may not love Sansa as he loved Cat he still protects her (partially because he has the hots for her and partially because she is Cat’s daughter), so he would not do something that would put her in danger that he didn’t believe she could get out of herself. He will not be around to actively protect her, since he will be back at the Vale. I don’t see why he pointed it out to the Boltons, even if he and Sansa know Arya is alive.
Arya’s fate is unknown. No one has specific reason to believe she’s dead. So Littlefinger isn’t breaking news.
Didn’t Brienne tell Sansa that Arya was alive?
Perhaps Littlefinger did love Catelyn at some point in the past, but we now know that he’s been scheming for power since prior to King Robert’s visit to Winterfell in show 1.1. I think it’s more probable that he discovered that the princes and princess were products of incest and then indirectly supplied Arryn with the vital info after which Jon began his investigation.
He then killed Jon knowing that the Lannisters would be the obvious suspects. He also had Lysa inform Catelyn that the Lannisters were behind Jon’s death (strategically after Ned had departed for King’s Landing). I can’t remember what initially made Ned look through the Baratheon family book to figure out the Lannister incest, but I wouldn’t be surprised if Littlefinger played a part in that. He knew that Lysa’s note would get Catelyn to King’s Landing to personally warn her husband. Remember that Littlefinger is the one who put the knife to Ned’s throat saying: “I told you not to trust me.” At this point, I think that Littlefinger was ready to pounce on Catelyn as a way to get power of the North, but since she rejected him he had to move on to the next plan.
The point I’m getting to is that I don’t think that anyone, including Cat or Sansa, were any more than pawns in his ultimate goal. Perhaps Cat’s initial rejection of Littlefinger in their youth led to his becoming the power hungry person that we all know and love (to hate).
This happened when Ned was in Winterfell. https://youtu.be/-XUIlY4V0Fw?t=3m45s
He’s also under sentence of death if he returns to Westeros. He’s deeply in love with Daenerys, and is certain that he just needs to right angle to win her back over. The brother of the man who killed her father (and served on the small council that sent assassins after her) is a pretty good place to start, in his mind.
Jorah doesn’t have a death sentence in Westeros. He was pardoned.
Thanks.
I never got the impression wants to run the kingdom. She wants what she imagines are the benefits of being queen but I don’t think that includes running the small council.
Why is revenge on the Boltons on Littlefinger’s bucket list?
They killed the only person he ever loved.
I’m not sure that revenge on the Boltons is on his bucket list, but that would be the reason.
I’m sure he’ll show up again eventually. (I have no spoiler knowledge.)
Who else is missing in action?
Bran and Rickon, and their associates, obviously. We’ll see them again, obviously.
Edmure Tully, presumably still hostage to Walder Frey.
Blackfish Tully, uncle of Cat, Edmure, etc. Missing since the Red Wedding, but I fully expect him to show up sooner or later.
Benjen Stark, Ned’s younger brother, Ranger of the Night’s Watch, unseen since season one. My theory is that he holds the secret of Jon Snow’s parentage, so I expect him to reappear when the plot requires him.
I thought Whore-Daenerys was hilarious, especially the assless dress. I loved how bored Olyvar was with the whole show too. 
Does Loras realize he’s in charge of King’s Landings most prominent brothel yet, or does he still think he’s just a squire who moonlights.
I just select “Add to dictionary” the first time I type and let auto-correct take care of the rest.
He think’s Daenerys will be so pleased at his delivering Tyrion to her she’ll forgave his treason.
In House Tyrell the men are just for show and breeding purposes; the women run everything from behind the scenes. Maergery is just applying what everything her grandmother taught her, and it seems like Tommen is going to be particularly easy for her to manipulate. 
So why would Jorah kidnap Tyrion to bring him to Daneruas? What would she want with him? And he was going there anyway, no?
Others have explained upthread why Jorah wants Tyrion. What I want to know is, how would Jorah of recognised Tyrion? They have never met on the show, Jorah was already in exile with the Dothraki at the start of season 1, and I get the impression he has already been there for some years.
So if they did ever meet it was many years ago and Tyrion now has a beard. Yes he is a dwarf but they are not that uncommon.
The Lannisters and Mormonts are two of the most important families in Westeros, so it’s quite likely that they attended the same kinds of social and official events. They likely both spent much of their lives in Kings Landing. Tyrion himself is quite famous. There’s no need for the show to explain exactly how and when Jorah learned to recognize Tyrion.
Jorah could recognize Varys - he worked for him, although it’s unclear he ever met him - and then pieced together who the dwarf must be. He also may have listened - for all Varys cautioned him, Tyrion basically told that whore who he was. “Oh, I was just recently one of the richest men in the world… I always pay my debts” - FFS, I cringed at that.
Why was it, by the way, that Tyrion couldn’t be with that whore? Was it heartbreak over Shae? A general inability to trust prostitutes after he got close to, and got burned by, two of them? Because that girl was a slave? Because his dick stopped working after the 400 gallons of alcohol he consumed on this trip?
I wouldn’t read too much into it, but by saying “eldest” he keeps his options open if another confirmed Stark kid turns up; it might damage his credibility later if he had flatly said that no other Stark kids remained alive. Primogeniture, beauty and marriageability still make Sansa the most valuable of the bunch.
Just what I thought, too.
I think that was left purposefully ambiguous. He saw Arya, certainly - but did he realize who she was, exactly? Maybe, maybe not.
Also notable, the non-nudity of Margaery stood out to me, especially after the gratuitous non-nudity of Danerys a couple episodes ago. The show threw in random nudity a few scenes later in the brothel seen, but it seems gunshy about nudity from its regulars at this point.