If you assume that the input values are centered at 0 (which is what the renormalization is doing), then you have ~ as many positive and negative values. So replacing them by 0 shouldn’t change much.
The max pooling is done on a 2x2 patch and convolution in general with 3x3 kernel and 1 padding.
So you mean that for example if we look at a patch on the left side of the image, the two values on the left are more often bigger than the ones on the right? Would you have code to check that? That is interesting.