Spelltwine would add up to three to a storm count. This is because you have spelltwine itself and the two copies of other spells that you have exiled, all of which are being cast.
The reason I say "up to three" is because there are two situations where Spelltwine will not be able to cast targets.
The target is no longer in the graveyard when Spelltwine resolves. Say your opponent were to use Elixir of Immortality while your Spelltwine is on stack, this would put their spell back into their deck, one of the targets to Spelltwine, preventing Spelltwine from exiling, and thus copying this spell. It would still exile and copy the target from your graveyard.
The spell being copied is illegal to cast. While timing rules are ignored for Spelltwine, since it forces the cast, other rules are not. You still must be able to legally cast the spell being copied. If you were to target Hex while there are 5 or less creatures in play or Decimate with no enchantments on the board, Spelltwine would still exile these cards, but you would be unable to cast the copies.
Since you mention Grapeshot, a card with storm, there's another point to make here. If you are casting a card that cares about spells cast before it using Spelltwine, like Grapeshot, you chose the order the exiled cards are to be cast. So you will have the Spelltwine itself counted either way, then can chose to cast the other two in any order. If you put Grapeshot first you get one less copy of Grapeshot. Remember last in, first out, so getting that extra Grapeshot would cause the Grapeshots to resolve first, if that matters for effects (say the other one cared about creatures and grapeshot clears a goblin army, or damage delt this turn)