One common plot is Arya being held prisoner by a powerful lord. She then has to find a way to escape while dealing with the lord's cruel demands. For example, he might force her to do menial tasks or endure his taunts.
Often, there's a plot where Arya's capture leads to a rescue mission. Her friends or family members, like Gendry or Sansa, hear about her capture and start planning to rescue her. This usually involves sneaking into the enemy's stronghold and facing many obstacles along the way. They might have to fight guards, avoid traps, and figure out how to free Arya without getting caught themselves.
In a fanfic where Arya gets captured, she might be used as a bargaining chip. Her captors could try to exchange her for something valuable, like a strategic location or a large sum of gold. Maybe they want to use her to manipulate the Starks.
If Arya is sent to the past, she might first try to find a way back to her own time. But in the meantime, she could end up influencing key historical events. Maybe she'd get involved with the Targaryen rule and change the course of their downfall. Or she could befriend some of the great warriors of the past and learn new fighting techniques that she could bring back with her if she ever returns to her own time.
In a fanfic where Arya gets pregnant, the first thing to consider is who the father might be. Given her character, it's hard to imagine her getting into a situation where she'd willingly have a relationship that would lead to pregnancy in the normal course of things. But if it did happen, it could be a plot device to show her vulnerability. She might struggle with the idea of bringing a child into the dangerous world she knows. And the people around her, like the Brotherhood without Banners or her remaining family members, would react in different ways, some with support and some with disappointment or shock.
She could change the fate of her family. Since she knows what will happen in the future, she could stop the execution of her father, Ned Stark. This would have a huge impact on the political situation in Westeros. The Stark family might gain more power and influence, and the War of the Five Kings might not even happen or at least take a very different form.
If Arya gets pregnant in a fanfic set in Westeros, it would be quite a shock. However, it could fit in if it was part of some grander scheme. Maybe she was used as a pawn by an enemy, and the pregnancy was a way to control her or her family. Or perhaps it was a result of a brief moment of weakness during her travels, and now she has to deal with the consequences in a world that isn't very forgiving towards women in such situations.
One possible storyline could be that Arya, being the resourceful character she is, tries to figure out how to hatch the dragon egg. She might embark on a journey to find ancient knowledge or a sorcerer who could help her. Maybe she faces many challenges along the way, like being hunted by those who want the egg for themselves.
One idea could be a story where Arya meets Lemon in a tavern during her travels. Maybe Lemon has some interesting information about Arya's enemies, and they form an unlikely alliance to take on a common foe.
She might get a small but fierce dragon, like a young and agile one. It could be a dragon with black scales, which would match Arya's dark and mysterious nature.
One common plotline is Arya's search for revenge. She might be on a mission to take down those who wronged her family, using her skills to hunt them one by one. Another is her journey to find a place where she truly belongs. Since she has been through so much, fanfic authors often explore her search for a home that accepts her for who she is.
Another plotline often involves the person she is betrothed to having to prove themselves worthy. For example, if it's a warrior, he might have to go on a dangerous quest or perform some great feat to win Arya's acceptance. This can involve battles and political intrigue within the world of Westeros.