Perhaps Sansa Stark accidentally gets sorted into one of the Hogwarts houses when she arrives in the wizarding world. She could be in Gryffindor, despite her more Slytherin - like qualities from her time in Westeros, and this could be a source of internal conflict for her. Harry Potter could help her come to terms with this new identity. Together, they could work on solving a mystery within Hogwarts that has ties to Sansa's past in Westeros, like an old magic that was once used in the Seven Kingdoms and has now resurfaced in the halls of Hogwarts. This would blend the two fictional universes in an interesting way.
One common theme is the clash of different cultures. Sansa from the medieval - like world of Westeros and the magical world of Harry Potter. Another could be the idea of power, as both universes deal with different forms of it.
Yes, there are quite a few. You can start by looking on fanfiction websites like Archive of Our Own. Just search for 'Harry Potter Sansa Stark' and you'll find a variety of stories that blend the two universes in interesting ways.
At first, Sansa might be a bit intimidated by Harry's status as a hero in the wizarding world. But she would quickly regain her composure and start to assert herself. Harry would respect her for that. They could interact in a way that combines their different skills. For instance, when facing a problem in the wizarding world that has elements of political intrigue, Sansa could step in and offer her insights, while Harry uses his magic to deal with the more dangerous magical aspects. Their conversations would be a blend of Sansa's refined language from Westeros and Harry's more modern wizarding world speech.
Well, a common plot point is the culture shock. Sansa, coming from a medieval - like world of Westeros, experiences the modern - ish (in a magical sense) world of Harry Potter. She might be shocked by things like the moving staircases or the talking portraits.
There are some fanfictions where Harry Potter and Sansa Stark meet through some magical portal. In these stories, Sansa is often amazed by the magic in the Harry Potter universe, and Harry is intrigued by Sansa's strong will and the different kind of courage she has developed in a world without magic but full of political intrigue.
In 'dark Sansa Stark fanfiction', Sansa can be more assertive. Unlike in the original where she is often a victim of circumstance, here she takes charge. For instance, she might not wait for others to rescue her but actively plot her own escape and revenge.
Another interesting one is 'A Pregnant Sansa in King's Landing'. This fanfiction takes a different approach. It focuses on Sansa's pregnancy while she's still in the heart of the political chaos in King's Landing. It shows how she uses her wits and strength, even in her pregnant state, to navigate the dangerous court politics.
It depends on the situation. In the wizarding world, Harry Potter would be more powerful as he can use magic which is a fundamental part of that universe. He can cast spells to defeat enemies, protect himself and others, and manipulate the environment around him.
Sansa would be more assertive in her political moves. She has seen the consequences of inaction and bad decisions in the future. So, she would be quicker to make decisions that benefit her family and herself. For example, she might be more involved in military strategies to protect the North.