The Batman character draws inspiration from a wide range of DC Comics. It's not tied to one particular comic. His traits and adventures are a combination of elements from various Batman-related publications.
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.
Definitely. Batman is a classic superhero character that emerged from the world of comics. His storylines and adventures have been developed and expanded over many comic issues.