Joey might be really impressed. He could be like a kid in a candy store, wanting to see how all the cool Batfam gadgets work. For instance, when he sees Batman's utility belt, he might be constantly asking questions about what each gadget does.
He may try to incorporate some of the ideas behind the Batfam's gadgets into his own fighting style or problem - solving methods. For example, if he sees how Robin uses his bo - staff with some added - on Bat - tech, Joey might think about ways to enhance his own weapon or abilities with similar technology - inspired ideas.
Joey could be an ordinary citizen who just happens to be in the wrong (or right) place at the wrong (or right) time and meets the Batfam. Maybe he's a journalist trying to get a scoop on the Batfam and ends up getting more than he bargained for.
Well, one possibility is that Joey could be in awe of the Batfam's reputation and skills. He might try to prove himself to them, perhaps by showing off some of his own unique abilities from the Teen Titans. For example, if Joey has some sort of special power like telekinesis, he could use it in a controlled way to gain their respect.
Well, perhaps Joey is a big fan of the Batfam in the fanfiction. So when he meets them, he fangirls/fanboys really hard at first. Then, as the story progresses, he gets to know them on a more personal level and discovers that they have their own quirks and insecurities just like regular people, which changes his perspective of them completely.
In the 'Spiderman meets the batfam fanfiction', it's possible that Spiderman would be intrigued by the Batfam's gadgets and their more brooding approach to crime - fighting. He might try to lighten the mood a bit. The Batfam, on the other hand, could be impressed by Spiderman's acrobatic skills and his quippy sense of humor. There could also be some interesting interactions between Spiderman and Robin, as they are both younger heroes in their respective universes.
Well, there could be epic battles. The Batfam's unique skills and the Justice League's superpowers would make for some intense fight scenes. Maybe Batman and Superman have a bit of a misunderstanding at first, with the Batfam trying to protect Gotham's interests while the League has a broader view.
In a 'justice league meets batfam fanfiction', there might be some interesting character interactions. For example, the Flash could be amazed by Robin's agility. Also, Wonder Woman might teach Batgirl some combat techniques. And there could be a lot of banter between the more light - hearted members of both groups, which would add some humor to the story.
Dick would probably be excited. He loves the idea of fans being so engaged with their world and would enjoy reading the different takes on their relationships. He might even leave positive comments if he could.
Seto's usually cold and calculating personality might soften. He could start showing more vulnerability around Joey. For example, he might let Joey see him without his usual confident facade when they're alone. Joey, on the other hand, might become more responsible. His impulsive nature could be tempered as he realizes he has someone he really cares about in Seto.
I think Robin could be very interesting. He's young and full of energy, and in a meeting with the Justice League, he could be in awe of them at first but then prove himself. He might learn new skills from the League members and also show them that the Batfam has its own strengths. For example, his acrobatics and quick thinking could come in handy during a mission, and his interactions with characters like Aquaman or Green Lantern could be really fun to read about.
Ross would probably be really shocked and a bit jealous at first. He might have a hard time accepting it. Phoebe would be super excited and would probably offer to be like a spiritual guide for the baby. Chandler would make a lot of jokes about it, but deep down he'd be happy for them. Monica would be practical and start planning things like baby showers and making sure Rachel has all the right things for the pregnancy.