Indian Killer is a novel by Sherman Alexie. It focuses on the life of John Smith, who was born to an Indian mother but was taken from her and given to a well-off white couple. As John grows up, he never quite feels comfortable with his identity. Eventually, he begins to believe that as an Indian, he'll never belong in mainstream, white culture. However, John also has no experience living with Native Americans. He is stuck between two worlds.
After moving to Seattle, John hatches a plan. He decides he will kill white people as a means of earning acceptance into Native American society. The results of John's actions shock mainstream society. Conservative talk show hosts demonize him. Native Americans begin criticizing whites and how they profit off of Native American lives and culture. Ultimately, John's actions spark a heated debate about how Native Americans and whites should live together in the modern world.
Your question about whether or not John is actually the killer is never answered by Sherman Alexie himself. However, John is explicitly named the killer in the novel within the novel, which is written by the character Jack Wilson. When thinking about the discussion in this novel, this makes sense. The white character, Jack Wilson, explicitly names the Indian, John, as the killer. However, Sherman Alexie, who is a Native American himself, does not do so. Perhaps Alexie is telling us, his readers, that the killings aren't as black and white as they appear to be.