After convolving, we would divide by the filter values sum in order to calculate the final pixel value? So for the 3x3 box filter, after convolving, we would divide by $\frac{1}{9}$ in order to come up with the corresponding pixel value?

^I imagine that this would only make sense if you want to maintain the same average intensity in the input/output? (for example, blurring or sharpening)

It seems very reasonable to have filters where this doesn't make sense; a finite difference filter, for example, would have values that sum to 0.

How would blurring and sharpening maintain the average intensity of input/output? Would the reduction in d_color not reduce intensity?