The Flash might initially be in denial. He's used to Batman always having a plan and his death would be a huge shock. He would then turn his speed into a tool for investigation, trying to find out exactly what happened. Green Lantern could feel a sense of loss but also be spurred into action, using his ring to try and prevent future tragedies like Batman's death. He might create constructs in Batman's memory to inspire the team.
Some of them might be amused. They could find the different takes on their characters and stories quite entertaining. For example, Superman might chuckle at a fanfic that has him in a comical situation.
He'd probably be confused at first. Naruto is used to being among friends and comrades. But then, his determination would kick in. He'd likely try to talk to them, to understand why they think he's a threat.
Some might be shocked. For instance, Batman is often portrayed in very different ways in fanfiction compared to his 'canon' self. Superman might raise an eyebrow at a fanfic where Batman is overly emotional. Others like the Flash might be really into it, finding the different takes on Batman's character and his adventures exciting.
The Justice League's reaction in fanfiction when Batman dies can vary greatly. Superman might become more withdrawn, feeling like he failed as a friend and protector. Wonder Woman could be the one to try and hold the team together, using her strength and wisdom. The Flash might struggle with guilt, thinking he could have been faster to save Batman. Each member would have their own internal conflict and way of dealing with the loss, which could lead to some interesting character development in the fanfiction.
Beast Boy would be quite distraught. He might initially feel a bit helpless, but then he'd start thinking of creative ways to find Robin. He could transform into various animals to search for clues or to sneak into Red X's lair. His sense of humor might also help to keep the team's spirits up during the search, even though they're all worried about Robin.
Batman could become more of an anti - hero. He might start working against the Justice League's interests, thinking that they have wronged him. He would use his skills and resources to expose any flaws in the League's operations and undermine their public image.
Sure, Teen Titans belongs to the DC Comics universe. They have had many adventures and storylines within the DC framework. DC Comics has developed and expanded the Teen Titans franchise over the years.