How does each copy of a spell cast to Zada, Hedron Grinder count towards Storm abilities?
Unfortunately no. Storm counts how many spells were cast, where Zada just copies spells already on the stack. 

Storm


  When you cast this spell, put a copy of it onto the stack for each other spell that was cast before it this turn. If the spell has any targets, you may choose new targets for any of the copies


Zada


  Whenever you cast an instant or sorcery spell that targets only Zada, Hedron Grinder, copy that spell for each other creature you control that the spell could target. Each copy targets a different one of those creatures.