Is add or ADHD considered a disability for a child?

Yes, if not treated. The best thing you can do as a parent of an add child is to treat it. The treatment, medication and behavior retraining is effective. So effective, in fact, that often it can erased the handicap and brings the child up to the level of his peers. Not treated, add can scar a child for life. Not sure if your child has add? Get him/her tested. Better safe than sorry!
Depends. It depends on what you mean by disability. Adhd definitely effects a child's academic performance if left untreated. Kids who have adhd usually qualify for 504 accommodations which means that the school must evaluate the child and determine what they can do to help the child with perform at his/her optimal level.
SHORT ANSWER. States and the federal government have laws that may allow a child to be considered able to get extra services--just as an example. But pure add/adhd in my opinion is not the norm. If slight depression is missed, stimulants may burn out. My point is if a child has things considered add they should have a full diagnostic eval with both a phd/psyd and md/do. Add is made worse by 200 plus med issues.
As in eligibility. For ssi? It was, about 25 years ago, if the person had significant learning disabilities. Disability is defined now by level of functioning & the level of support needed for a person to function within a community. ~70% of cases of adhd have 1 or more comorbid psychiatric, neurodevelopmental or chronic medical condition. Ssi requires all med, psych & school records & has their own testing done.