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How exactly is the basket raised up to goal top level?
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There are two pivot points... One is located where the basket meets the arm and the other where the arm meets the metal thing
that attaches it to the base. Powered by a drill motor (brakes on) with
[Edit: some major gear reduction], the arm-base pivot allows the arm to go forward and back to become parallel to the goal. Powered by two globe (?) motors, the basket-arm pivot allows the basket to go down and up to become parallel with the floor. In the end, you have the arm aligned with the goal, and the basket at a position where gravity does some of the work in dumping the balls. Oh... to dump, the arm operator drops the bar at the back of the basket, which holds the balls in, and holds the trigger button on his joystick, as though he is picking up the balls. If you need something more detailed than this, you'll have to ask Steve.
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...what is that surgical tubing used for?
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The surgical tubing functions as a brace for the basket. When the basket is filled with balls, gravity tends to pull it towards the floor. This forces our arm driver to constantly reach a compromise. This wasn't acceptable because we wanted the arm driver to worry about dumping the balls, not holding the basket up there.
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...where do you get this polycord stuff?
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I think the mechanical people got it from the small parts catalogue.