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I think that the survivors were brought on that island because they are all connected to each other and they should know each other but they don't. They're too busy focusing on themselves to pay attention.

You know how the pilot told Jack and Kate in the very first episode that they were having problems with the plane and they tried to land in Fiji and by the time they hit turbulance they were 1,000 miles off course. Well, I think that the Pilot works for Dharma and crashed the plane on purpose. All the others work for Dharma and made sure that the planed crashed on their island so that they could conduct experiments on the survivors. That's why the psychic told Claire to go to LA on flight 815 , he knew the whole time. That's why at first he wouldn't give the reading because he wanted to protect her. And Sun's father telling Jin to go to LA to deliver a watch to one of his friends. he knew that they were planning to run away.

The people at Dharma are psychic and wanted to see how the survivors get along in certain situations. They knew Walt had special powers and so they used him to create the situations. The whole thing is an experiment on society. They want to change it and try to make it better.

They kidnapped Claire to lead Locke and boone to the hatch so that they would open it. They also made them press the button to see how gullible they are and whether or not they will follow orders. When the button isn't pushed they release a jult of magnetic power ( that's how they gave the illusion of turbulance)

Have you noticed that everyone is in a different situation (except everyone has issues with their dad or sometimes mom). There's one doctor, convict, conman, addict, torturer, single soon-to-be-mom, etc. that's also part of their experiment.

They kidnap children because they want to see how far someone will go to save to save their children.

They either kill or brainwash people after their done experimenting them.

They got the numbers from every number from the crash and people's lives. ex: flight 815, Jack's seat was set 23, Ana-Lucia's was 42, the plane crashed in september. And the reason Hurley's friend from the mental hospitol repeats the numbers is because he was taken by Dharma, brainwashed and sent back, but the only thing he remembers is the numbers.