Can kids go on diets?

Depends on age. If you have an obese infant, it is still important to provide a minimum amount of calories and breastmilk or formula mixed to the right concentration to avoid electrolyte abnormalities. Older children can be placed on diets, but it is important to have this catered to the age of the child so that he or she is still getting in enough of the right calories + nutrition for adequate growth.
Yes. Excess weight is a common problem in children. They frequently follow the example of their parents who are often overweight as well. Children can go on diets and should be encouraged to do so if they are obviously gaining weight. Enlist the aid of your pediatrician and a good nutritionist.