Financial gain might be another reason. They could be trying to extort money from the airline or the government. Also, personal grudges against the airline or someone associated with the flight can't be ruled out. For example, if an employee had a bad experience with the airline and decided to take extreme measures.
Since it's based on a true story, there are likely many elements to it. It could start with the planning of the hijackers. They might have chosen flight 601 for a particular reason, like its destination or the type of passengers it usually carried. Once the hijacking occurred, the crew and passengers would have been in a state of panic. The authorities would then be involved in negotiations or rescue attempts. There could also be international implications depending on the origin and destination of the flight. But again, without more information, it's all just speculation.
Not necessarily. Many stories claim to be based on true events, but 'Flight' might have taken liberties in the storytelling to make it more engaging or to fit a certain narrative structure.