Part 2

You can use the blend tool along with the pathfinder pallet to divide shapes.

You can divide a circle into a set number of slices or divide a square diagonally.

To divide a shape into squares (or pixels) you can take two blends at 90 degrees to each other then expand them. Next place them over the shape to be divided and select the whole group. Next use the pathfinder division tool to divide all the shapes.

You can then ungroup and delete every second square to give a checker board effect.