That “what if the Starklings were all girlsl?” AU has taken a life of its own. A compilation of some asks under the cut:

On the karstarks  status as a consort candidate- Lord Karstark already
thinks himself above Robb in canon (killing the prisoners) I definitely
don’t see him deferring to his teenage daughter in-law. 

Did he though? Up until his son’s death and Jaime’s release, there was
no indication whatsoever that Rickard Karstark thought himself above
Robb. Even when the rest of the lords were transparently testing Robb
back in AGoT, Rickard is conspicuously absent from the list of people
Bran noted tried to push Robb. I mean, Roose Bolton brusquely demanded command, Maege Mormont told Robb he has no business giving her orders because he was young enough to be her grandson, the Greatjon even went as far as threatening to leave if he was put behind others, but of Rickard Karstark, there was no mention of a challenge. Karstark was also the second man to declare for Robb as King on the North after the Greatjon, and while he stormed out of the hall while Robb gave Cleos Frey his peace terms, he did nothing to try to stop it, nor did he challenge Robb over it. It wasn’t until Jaime was released and Catelyn was pardoned that he went against Robb and killed the prisoners. While everything about that was despicable, it’s hardly evidence that Rickard’s baseline was thinking that he was above Robb.

Weirdly your Robin AU is what I want for the series. The Lady of
Winterfell and her bastard brother leading her armies (& husband I
assume she marries quick). What happens at the Freys when they need to
cross? Does Cat go south if Robin stays? Would Robin ride to war (Like
Black Ally or the Mormonts?)
       
    

You know, I love the thought of it, especially as I’ve said that I think Ned would be promoting the image of Jon as his sisters’ champion. But, and I don’t mean to rain on your parade, Jon definitely still goes to the Night’s Watch in this scenario. Like I said, Catelyn would fear the danger he could pose to her line’s right to Winterfell even more if she only had daughters and so the events of Jon asking to join Benjen and Catelyn insisting he can’t stay probably happen like in canon. And even if Ned refuses and has Jon stay to look out for his sisters, he wouldn’t be the one leading the army because giving a 14-year-old bastard the command would be an insult to the experienced and battle-hardened Northern lords.

As for the Freys, assuming Robin is already betrothed (and I think she would be), it’s Edmure’s hand that would be Walder Frey’s price. He does drop hints about Edmure in his conversation with Catelyn in canon after all. But a problem would arise in that Catelyn doesn’t really have the authority to promise Edmure’s hand at a time where Edmure is trapped on the other side of the Green Fork unable to give or withhold consent.

I’ve said before that I highly doubt that Robin would be taking the field but she’d probably still go with her army because, as Robb said in OTL, Ned wouldn’t have sent men to die while he stayed behind, and while she can’t fight physically, she can at least make sure her men don’t die for a stranger. That’s her father and sisters that have been imprisoned and her call that the bannermen have answered. She isn’t sending men to fight in the name of her family while she stays behind in Winterfell.

I can see Robb as a girl not being trained with weapons but wouldn’t
strategy and logistics be part and parcel of being a ruler? Cat has a
good grasp of them herself & her father stopped teaching her at 12.
Medieval women were historically very involved in warfare (if only in
sieges).

Yes, you’re correct. I got tangled in the thought that an heiress or a ruling lady would be expected to delegate such responsibility to a trusted lieutenant and thus giving her that training wouldn’t be priority in a patriarchal society that sees this as a job for a man. I asked @warsofasoiaf for his opinion since his knowledge of both feudal politics and strategy surpasses my own by miles, and he agrees with you. To paraphrase Jim’s answer: while the decision of the extent of a lady’s education in strategy would be up to her instructors (i.e, whether she’d be given the standard education or just taught how to exert authority but not to necessarily make plans with the expectation that the planning would be delegated to her lieutenant), overall planning is probably something she’d be taught.

(Btw, where was it said that Hoster stopped teaching Catelyn at 12? She was
betrothed at 12 but she’d have stopped being the heir by Edmure’s birth,
and Edmure was definitely born before Cat was 12.)

Bran’s storyline doesn’t change much if he is a girl neither does
Rickon. How do Arya & Sansa deal with having other sisters?
       
   

It would benefit them. Sansa would have an older sister to look up to and wouldn’t put all her expectations of a gender-conforming sister on Arya which means their clashes would go down and their relationship would not be as tense as canon. While that does not mean that Sansa wouldn’t still disapprove of her younger sister, the bullying that Arya suffers goes down significantly as does the weight of Sansa’s expectations.

I’m guessing Robin might also be a good middle-woman between Sansa and Arya as her education would combine the traditionally feminine aspects that appeal to Sansa – fostering a good relationship between the two eldest girls – with the heir training that would involve things that are seen as traditionally masculine, making it that Arya is not made to feel like there is something wrong with her for not conforming. After all, if Robin is expected and encouraged to attend executions or learn warfare, then there is nothing inherently wrong with having interests that are deemed “manly” by the wider Westerosi society. Mind you, that does not magically lift all expectations off Arya’s shoulders, neither would she be encouraged to pursue such activities , but perhaps it would make things less suffocating for her. As for Sansa, having an older sister who is close to her age and shares some interests means that there would be a line of communication between the two girls, so perhaps Robin’s more realistic view of the world might temper Sansa’s “beauty equals integrity” mindset. Maybe.