Is there only one area at the airport where the shuttle stops, whether to drop off or pick up customers?

Yes there is only 1 area, which is at the pink Pilars. Each terminal has 1 pink Pilar, and it is located on the lower level.

you are allowed to change your reservation up to 2 hours before you fly.

Shuttle only picks up and drops off at the lower level arrival area at each LAX terminal.