As of now, no. In the Boruto series, their relationship is mainly focused on their friendship and comradeship as ninja. There are some moments that fans might interpret as having a hint of something more, but the story has not made their relationship a romantic one in an official capacity.
Well, it's not necessarily the absolute end. It could be a cliffhanger or a way to create suspense. Sometimes in anime, they say things like this to make the audience think about what might come next. Boruto might face new challenges that are even greater, and this statement is just a pause in the story. For example, there could be a new villain emerging from the shadows, and this 'end' is just the calm before the storm.
No, Boruto is alive in the manga. The plot hasn't led to his death. However, the manga is ongoing, and anything could happen in the later developments.
It could be a rogue ninja who has a personal vendetta against Boruto's family. This ninja might have caused harm to Boruto's father Naruto in the past, and now Boruto is determined to make him pay.
It could be the Kara organization. They've been shown to be interested in Boruto's Karma mark in the original series, so they might have finally made a move to abduct him in the fanfic.
In a 'naruto dies boruto fanfic', Boruto's character would go through a major transformation. He would be forced to grow up overnight. Initially, he might be consumed by anger and a desire for revenge if Naruto was killed unjustly. But as time passes, he would learn to channel that energy into positive change. He would study his father's leadership style and try to implement it in his own way. He would become more diplomatic, forging alliances with other villages to strengthen Konoha's position. His sense of justice would be refined, and he would be more committed to protecting the world his father loved so much.
Boruto's character development could be a complex journey. At first, he may feel overshadowed by his parents' fame and power. This could lead to him acting out or trying to prove himself in the wrong ways. However, as he experiences more of the ninja world and faces challenges, he starts to understand the true meaning of his parents' actions. He might develop a more empathetic side, seeing things from the perspective of others, especially those affected by Naruto and Sasuke's past actions. He also grows in terms of his combat skills, learning from both his father's brute force and Sasuke's finesse. His character arc could be about finding his own identity within the context of his parents' great reputations.
In the Boruto manga, the story is evolving with complex plotlines. New villains are emerging, and Boruto is growing stronger as he navigates through various obstacles. The relationships between characters are also deepening.