Blot water and remove eggshell bits with a paper towel. Kids love to use this gadget, popping egg shreds into the bowl.
Personal preference varies.
Da Bunny likes enough so that the egg mixture just sort of looks appetizing and handles with ease. Salt and Pepper to taste. Egg salad on crackers is yummy. I'd rather use a fine fresh grind, if I am going to be fussy. What's fun about Easter Egg Salad is that the egg whites often have absorbed a bit of color, so it's like having Confetti Sandwiches.