Depends. Many obese adhd kids eat themselves into obesity because they are unable to inhibit (a primary symptom of adhd) and lose weight when treated because they can learn to eat properly. Losing weight, per se, will not help adhd. The only dietary modifications that help adhd kids is the avoidance of caffeine or chocolate.
Absolutely. Both diet and specific supplementation are very useful, and very helpful. Weight loss goes hand in hand with proper dietary modification.
It may in some. There was a budding industry years ago around the Finegold" diet that attributed the problems to sugar and other food. This has been debunked over the years. Any person performs at their best with proper nutrition, rest and health. Any dietary deficiencies should be recognized and fixed. Some kids over consume partly because they aren't meeting their nutritional needs.