Definitely. Batman and Superman have long been featured in DC Comics, and the movie takes inspiration from those comic sources. It incorporates elements and plot points from various comic story arcs.
Batman vs Superman isn't based on just one comic. It's a theme that's been touched upon in numerous DC comics, each adding its own twist and take on the confrontation.
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.