I am not sure if the stones will continue to be a problem if you keep her on the same diet. There is special urinary diets that you can get but I am not sure when he would be able to go on them becuase he is still so young and will need a higher energy diet. Also the stones can be sent into a lab to determine just what they are made of to help. The surgery needs to be done, it is painful - Imagine rocks in your bladder always irritating it. The potty training should go way better once he is stone free :) GOOD LUCK WITH HIM! :)
I assume you mean bladder stones? I couldn't tell you about how often they may return or not, but you might post that question to Dr. Cheng on the Ask a Vet forum. She generally answers questions in the early evening hours.
As for the stones, that can be a very painful condition, and you'll probably notice an immediate difference after surgery. Once the stones are analyzed in pathology, you'll know what kind of material is in them, and may be able to control future problems with diet.