Do spell copies (à la {Pyromancer Ascension}) count towards a Storm count? (Reference, {Grapeshot})
That depends. If you use an effect like {Twincast}, you'll just put the copy straight onto the stack, and since you didn't cast it, it won't count towards storm. If you have an effect where you cast a copy, like {Elite Arcanist}, then it will count towards storm.
111.1a (http://imtgapp.com/forum/index.php?action=imtg;area=rule;number=111.1a): A copy of a spell is also a spell, even if it has no card associated with it. See rule 706.10.
Edit: {Pyromancer Ascension} is like {Twincast}, so its copies don't count.
Nope (unfortunately), storm counts spells CAST, {Pyromancer Ascension} copies spells, it doesn't cast them.