1. Do you know how to find the minimum value of a function? You differentiate it and set the derivative to 0. This will give you both maximum and minimum values, but if you already know the function can't have a maximum, you can assume that you've found a minimum.
2. See the diagram at the right. You can see that if P is moved a little, so that the two vectors are no longer perpendicular, the distance from P to Q would get longer.
3. They come from the components of the vector pVQ.