Since you mentioned that Sansa is mostly like Ned in terms of personality, which i agree 100%, how do you think Ned and Sansa's relationship was like?
Ooh, interesting question. Well, at least on the surface, I think Sansa was one of his children Ned felt like he had to worry about the least. Robb would get a lot of attention as Ned’s heir, of course, and it’s also Ned’s job to train Bran and eventually Rickon as Northern lords ready to take over the running of Winterfell as a just-in-case policy, as Ned himself - also a younger son - was forced to do after his older brother’s death. (Which we see with Bran being required to attend that beheading way back when, for example.) Arya is the wild child, getting extra attention both because of her resemblance to Lyanna and in the general sense that ‘the squeaky wheel gets the grease.’ And Jon is obviously a separate issue and gigantic can of worms all on his own.
So where does that leave Sansa? She’s a good girl, she’s pretty and smart and well-behaved, and she wants to be the thing she’s supposed to be: a lady. And because she’s a girl, her education is already the provenance of her mother, not her father; it’s Catelyn’s job to make sure Sansa knows what she needs to know about manners and graces and running a household and so on, not Ned’s - for one thing, he wouldn’t know where to start. And we see the effects of this on the current narrative, where Sansa is more likely to refer to her mother than her father as a role model - “I must be strong, like my lady mother” and etc. So I can see where some people might get the idea that these two had a relatively more distant relationship than Ned and his other kids.
But…am I going to stop there? Haha, of course not. Because like I said, Ned and Sansa also seem to have the most similar personalities of all the Starks. Here’s a GoT quote from one of the Bran sections to think about:
He [Ned] had a grim cast to his grey eyes this day, and he seemed not at all the man who would sit before the fire in the evening and talk softly of the age of heroes and the children of the forest.
This is interesting for a couple reasons. One is that we have Bran commenting on Ned’s apparent ability to slip in and out of different personalities depending on the role requiring of him - an ability that Sansa will soon need to develop. Another is that it gives us definite evidence that Ned, for all his supposedly grim and gloomy personality, also had an affection for songs and stories that even extending to telling them. And the other Stark with the most noted love of stories is, of course, Sansa. I wouldn’t be at all surprised if part of Sansa’s love for storytelling comes at least in part from memories of her father sharing these tales with her and her siblings.
Here’s another GoT Bran quote:
He had taken off Father’s face, Bran thought, and donned the face of Lord Stark of Winterfell.
Once again, this is Ned showing his ability to compartmentalize different parts of his personality in order to get the job done - the exact same ability that Sansa will come to develop (somewhat to excess) later in her life. She didn’t learn this trick from Catelyn; Cat was smart and tough and savvy but emotionally far healthier and less repressed than her husband, and never showed much evidence of Ned’s (probably trauma-acquired) neat trick of packing up his emotions and putting them away till later. Sansa develops this same trick mainly as a result of her own trauma, of course - but with the help, I would argue, of her father’s behavior to base it on. It’s honestly pretty impressive that despite everything she’s been through and all the intense repression and denial of feelings she’s been forced into, Sansa still hasn’t gone crazy - and part of that might be because she had a positive role model like Ned to show her that you can compartmentalize without losing yourself in the process. Sansa has always been very observant, and whether she realized it or not, I think she watched her father very closely and unconsciously picked up on a lot of his subtle coping mechanisms as a child.
As far as Ned himself, I don’t know that he ever fully realized how similar Sansa was to him - given her youth and gender, there weren’t a lot of chances for her to show it off, you know? But I would bet that Ned had at least a few moments of looking at his daughter and getting that dizzying sense of looking at his younger self - her stubborn insistence that Joffrey is her ‘one true love,’ for example, isn’t that far off from Ned’s own blind devotion to Robert and refusal to see his friend’s flaws when he was a young man.
It’s always harder for a parent to deal with the children that are most like them rather than the children least like them, and in my opinion that contributed somewhat to Ned’s difficulty in making Sansa understand him at that time (though honestly every adult in her life did a terrible job of explaining things to Sansa, he was far from alone). It’s rarely pleasant to have your own flaws reflected back at you from your offspring, and it’s pretty understandable that Ned struggled to get through to Sansa in that instance, considering how much he was still struggling to get past his own idealized version of Robert. So there was certainly room for conflict between the two of them as a result of their similarities, and if Ned had lived and Sansa had had a normal teenagerhood I’m sure this would have developed further, as it usually does in pretty much all families with a teenager.
But in the end? Ned was devoted to Sansa, just like he was to all his children, and Sansa adored Ned. It was a loving and healthy father-daughter relationship - and, like all the Stark relationships, pretty remarkable, given the extent of the dysfunction we’ve seen in the families of the other noble Houses. (Yikes, I’m going to tear up just writing this. You are missed, Ned.)
Sidenote: I drew from another online article when writing this, which is where I took my two book quotes from, but I have unfortunately misplaced the link; if I manage to find it again, I will add it here, and if not, apologies for the lack of citation.