One main theme is the struggle for power. Just like in 'A Game of Thrones' where various houses fight for the Iron Throne, in the fanfiction set in the 'A War of Stars' universe, different factions might fight for control of a planet or a star system. Another theme is loyalty. Characters have to decide who to side with, whether it's their own family like in 'A Game of Thrones' or a particular group in the 'A War of Stars' context.
Sure. One great 'A Game of Thrones' and 'A War of Stars' fanfiction is 'The Throne in the Stars' on FanFiction.net. It combines the political intrigue of 'A Game of Thrones' with the epic space battles of 'A War of Stars' in a really interesting way.
One idea could be a story where Kratos finds himself in the world of Westeros. Maybe he gets involved in the power struggles between the houses. He could use his combat skills to fight against the White Walkers, bringing a whole new level of action to the fight against the undead.
The desolate and harsh landscapes of God of War could be blended with the diverse regions of Westeros. For instance, the frozen wastelands where the White Walkers roam could be combined with the ice - covered areas in God of War. This would create a more extreme and dangerous environment for the characters.
One way is through the characters. Kratos could enter Westeros through a portal or some magical means. His brute strength and combat skills would immediately change the power dynamics. He could be a wild card in the wars for the throne.
A 'God of War' and 'Game of Thrones' fanfiction might feature a crossover of their mythologies. The gods in 'God of War' could interact with the Seven in Westeros. For example, Zeus could have some sort of encounter with the High Sparrow. Kratos might also have a unique perspective on the power struggles in the Seven Kingdoms, having dealt with his own power - hungry gods in his world.
Division within a society is a big theme. In 'Game of Thrones US Civil War fanfiction', the kingdoms or factions are often divided, like the North and South in the US Civil War. There's also the theme of sacrifice. People are forced to give up things they hold dear for the sake of their cause, similar to what happened in the real - life war.
Arya Stark would be a great choice. You could write about her using her assassin skills to target key military leaders during the war. For example, she could infiltrate enemy camps disguised as someone else and take out important commanders, which would have a huge impact on the battles.
One idea could be a story where the Starks form an unexpected alliance with the Greyjoys to take on the Lannisters. They could use the Iron Islands' naval power and the Stark's knowledge of the North's terrain to launch surprise attacks.
If Robb won the war in a fanfic, it could lead to a completely different Westeros. He might establish a more just rule in the North and perhaps even expand his influence over other kingdoms. Maybe he'd form new alliances and bring about an era of peace and prosperity, unlike the chaos that followed in the original series.