Not exactly. Batman Begins is one interpretation of Batman's origin story, but it's not the definitive or only 'real' one. Different Batman stories and adaptations offer various takes.
Well, Batman's origin story often involves the trauma of witnessing his parents' murder. This event drove him to train and develop the skills and gadgets needed to become the Dark Knight.
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.