Sure was. Batman Beyond was indeed a comic that explored the adventures of a new Batman in a dystopian future. It had unique storylines and art styles that attracted many fans.
A really cool 'Batman Beyond' fanfiction is 'Future of Gotham'. This one takes a look at the future of Gotham City itself, with Terry as Batman facing threats that could change the city forever. It has a unique take on the technology in the 'Batman Beyond' universe.
One of the best is 'Return of the Joker'. It delved deep into the complex relationship between Batman and the Joker, even in this futuristic setting. It was dark, full of twists, and really explored the legacy of the original Batman - Joker dynamic.
There's no fixed number of Batman Beyond comics. It's a constantly evolving field. Different story arcs and special editions contribute to the total, making it difficult to provide a precise count.
Damian would likely become more cynical in the Batman Beyond setting. The darker, more technologically advanced yet decaying Gotham would harden his already tough personality. He'd probably be less trusting, especially with all the new threats that come with advanced technology.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). There are many talented writers who post their 'Batman Beyond' fanfics there. Just search for 'Batman Beyond' in the search bar and you'll find a bunch of stories.