Your question depends on which side of the square you are facing(assuming you are using clockwise winding). When you create a polygon, by specifying the winding of the polygon, you are telling Opengl(or directx or whatever) that a polygon has 2 sides; a front and a back face(this allows you to see the inside of a box if you leave 1 face missing). When you use a specific culling mode(you could use no cull mode and then not worry about any of this) you are telling the graphics API not to draw a backface. So how does this apply to your question? Lets look at just 1 of your squares:
0---1
| |
| |
2---3

If we say that this is the front of the square, then we would use these indices to create that effect: 013, 032 or whatever order you prefer, as long as they are being wound clockwise. However, to make this the backface, you would use the winding: 102, 231. Now you would not see the polygon, as you are removing backfaces by using backface culling. I hope this is enough to help you figure out your question. If you are confused, feel free to inquire some more!

Yes, The normal is for lighting only. The ''winding'' of the vertices is what determines the front or back of a face/triangle.