Strange noise deviation formula
I can answer the first part of your question: Where formula 2(3) comes from.

Since the noise model is Laplacian, you are looking at an estimate of the standard deviation of a Laplace distribution. Compare the moments equation on this Wikipedia page: http://en.wikipedia.org/wiki/Laplace_distribution#Moments

As for what N is, it looks like they define it as a matrix operator in 2(2). So the sum in 2(3) is taken over pixels of an image generated by convolving the original image I(x,y) with the Laplacian operator N (which is denoted by $I(x,y)*N$, where $*$ is the convolution operator).