Sorry i'm pretty new to this pool stuff... but i can definitely tell the caulking area between the coping and the pool deck needs repairs. That sounds rather easy... just yank out the old stuff, pour sand in it, and put caulk in. Maybe put sand on top of the caulk or use a special kind of caulk?
But what about the coping around the pool, the stones and grout. It looks like there are cracks all over, and if I stomp on some of them they either move a little or sound hollow.