She could be a key figure in uniting the Seven Kingdoms under a new form of government. Instead of the traditional monarchy, she might propose a council - based system where each kingdom has a representative. Her diplomatic skills and her family name would give her the credibility to bring all the kingdoms to the table and discuss such a major change.
If Sansa gives birth, it could solidify her claim to power in the North. A new heir means a continuation of her line, which would make it harder for any rival houses to try and usurp her position. Other regions might also view her differently. For instance, the Vale which has been an ally might become even more closely tied to the North. They could see the new heir as a way to further their own influence in the future of Westeros through marriage alliances.
The Lich King could be a major disruptor. He doesn't care about the normal politics of the Iron Throne or the houses. He would likely try to use the political chaos to his advantage. For example, he could support one side in a war just to create more death and destruction, which he can then use to raise more undead soldiers.
Gunpowder can change the political landscape by giving an edge to those who possess it. For instance, a minor house with gunpowder can threaten larger houses and demand concessions. It could lead to new alliances being formed as houses seek protection from or access to gunpowder. Also, it might make traditional military strategies obsolete, forcing lords to rethink how they defend their lands.
One possible plot could be that Sansa's adopted daughter is from a noble but fallen house. Sansa takes her in to show mercy and to strengthen her own position in the North. The girl could be a target for rival houses, and Sansa has to fight to protect her. This could lead to political intrigue and battles as Sansa uses her wits and influence to safeguard her adopted daughter.
The OC could introduce new ideas to Sansa. For instance, if the OC is well - traveled, they might share stories of different cultures and ways of life that make Sansa more open - minded. This could help her grow out of her more sheltered view of the world.
Often, Sansa is portrayed as a powerful figure in fanfiction, and Jaime's character can add an interesting dynamic. They might be shown as having conversations that never occurred in the show. For example, Jaime could offer Sansa his insights about the political situation in King's Landing, which she could use to her advantage in her own political maneuvers in the North.
She could have a major impact on the political landscape. If she is a strong - willed character, she might be able to sway the opinions of the lords and ladies. For instance, she could use her charm and intelligence to convince some houses to side with the Starks in their battles against their enemies.
A pregnancy for Sansa in relation to Jaime would completely shift their story arcs. For Jaime, it could be the ultimate test of his new - found moral compass. He has already broken away from some of his family's more cruel ways, and this would be another step in that journey. For Sansa, it would add another layer of vulnerability and strength. She has grown from a naive girl into a strong woman, and a pregnancy would force her to be even more resilient. It could also lead to some interesting interactions with other characters, like Tyrion who has his own complex relationship with both Jaime and Sansa.
The powers of the X - Men would have a huge impact. For instance, Jean Grey's telekinetic and telepathic powers. She could easily manipulate the minds of the lords and ladies, making them vote or act in a certain way. This would completely disrupt the normal political intrigue and power plays that are based on alliances and manipulation through words and gold. It could lead to a new form of rule where those with the most powerful mutants are in control.
One possibility for Sansa's adopted sister in fanfiction is that she could be a spy. Maybe she was adopted by the Starks under false pretenses, but actually sent by an enemy. However, as she grows up with Sansa, she starts to have a change of heart. She could then use her position to feed false information back to her original masters, all while protecting Sansa and the Stark family from harm.