If a child is given ADHD meds of different types, and none work, is it safe to say that ADHD is not the problem?

It suggests so. Not completely but it certainly raises that possibility. But remember some meds work for 1 patient and not another.But make sure your evaluation is done by a trained professional. Also some patients have add/adhd but also other coexisting diagnoses such as anxiety, ocd , etc.
Needs evaluation. No , he should be evaluated by neuro develop mentalist, psychiatrist or your pediatrician.
ADHD is complex. Adhd must be differentiated from many other conditions & often is comorbid with (accompanies) many other conditions. Response to adhd meds does not confirm a DX & lack of response doesn't mean the person doesn't have adhd. A detailed evaluation & treatment by a skilled professional is necessary. Some children will not respond to the adhd meds before age 6 but may respond later as they develop.