Luke's character would develop a darker side, not in terms of being evil, but in having to face the inner turmoil of his vampiric existence. He'd have to constantly fight the urge to feed, which could make him more empathetic towards those who struggle with their own inner demons. His relationships with other characters would change significantly. Han and Leia might be hesitant to trust him at first, but as he proves himself, they'd come to accept him again. His physical abilities would also change, and he'd have to adapt his fighting style to his new vampire - enhanced strength and speed.
When traveling to the future, Luke could become more desperate. Facing a world in chaos or a new, powerful enemy, he'd have to quickly adapt and find solutions. This would make him more willing to take risks and use powers in ways he hadn't before. His view of the Force might also expand as he encounters new forms of it in the future.
Luke joining the Empire in a fanfic would be a huge shift for his character. His naivete might be exploited by the Empire. He could be made to believe that the Empire's way was the only way to bring order to the galaxy. As he got more involved, he'd see the atrocities committed by the Empire. This would cause him to reevaluate his decision. His character development would then be about redemption, trying to make up for the wrongs he'd done while with the Empire. He might even try to use his position within the Empire to undermine it from the inside, which would be a very different kind of hero's journey from what we're used to in the Star Wars franchise.
The relationship could develop in a complex way. Since Vader has captured Luke, there's a power imbalance. However, as they interact, Luke might try to reach out to the good in Vader. Vader, in turn, might be conflicted. He could start to protect Luke from the Emperor's harsher plans, leading to a strange alliance within the captivity.
Luke would likely develop a deeper understanding of the Jedi's roots. This could make him more traditional in his approach to the Force, or it could make him question some of the Jedi teachings he learned in his own time. Leia, on the other hand, might develop a more global view of the galaxy. Instead of just focusing on the Rebellion, she could see how different factions interacted throughout history, which would shape her leadership style in new ways. For instance, if she saw how the Sith influenced events from the shadows in the past, she would be more vigilant in her own time.
In fanfiction, their relationship could develop more quickly towards mutual understanding. Maybe Luke could convince Vader to turn away from the dark side much earlier, and they could start training together as Jedi. This would be a huge shift from the original story.
One plot idea could be Luke being turned into a vampire during a secret Sith experiment on a remote planet. He then has to struggle with his newfound vampiric instincts while still trying to uphold the Jedi way. Another could be that he is bitten by a vampire - like alien species and has to find a cure before he fully succumbs to the dark side of his new nature. Maybe he forms an alliance with some outcast vampires who also oppose the Sith's evil plans.
As they go on adventures together, their bond would strengthen. They could face a great enemy like a powerful dark side user. In the heat of battle, they would rely on each other and start to trust more deeply. Ahsoka might see some of Anakin in Luke, which would make her more protective of him, and Luke would see Ahsoka as a wise mentor figure.
Well, in certain Star Wars fanfictions, Rebel Luke Skywalker is presented as a more complex character. He could be struggling with the darker side of the Force more than in the movies. This internal struggle might make him question his actions and decisions more often. It also adds an interesting layer to his character as he tries to balance his growing power with his loyalty to the Rebel cause. He may face moral dilemmas, like whether to use certain Force powers that could have negative consequences but would benefit the Rebellion in the short term.
His character would develop in a very different direction. He'd be more independent and self - reliant. No longer bound by the strict Jedi code, he could explore the darker aspects of his personality. He might become more cynical and worldly. His skills with a lightsaber could be used more for intimidation and self - defense in the cutthroat pirate world. His view of the Force might also change, seeing it as a tool to gain power and wealth rather than just a spiritual guide.
His relationship might develop with a lot of forgiveness. If his father is part of the family reunion, Luke may have to forgive his past wrongdoings. They could start to train together, strengthening their bond through the sharing of Jedi knowledge.