Q. Explain the NCP and explain the difference between the green and white announcements ?
Is this something to do with the auto pilot ?
You probably mean MCP (Mode Control Panel). The "green and white announcements" are the FMA (Flight Mode Annunciators) with respect to what has been selected on the MCP. The white annunciator means that the mode in question is armed and 'waiting' to be captured. The green annunciator means that the mode is captured.
Q. Why do we have different segments for take off ?
The following links may help. Using the search function can go a long way!
Departure Segments [Archive] - PPRuNe Forums
Take Off and Climb Segments...? [Archive] - PPRuNe Forums