If you cast Seize the Storm with no instant or sorcery cards in your graveyard and no cards with flashback in exile, the Elemental will start as a 0/0 creature. However, state-based actions won't be checked until after Seize the Storm has finished resolving. The Elemental will then be a 1/1 creature and survive because Seize the Storm will either be in your graveyard or in exile.

While a spell is on the stack, it is neither in your graveyard nor in exile, so it won't contribute to the Elemental's power and toughness. For example, with Seize the Storm in your graveyard and no cards in exile, the 1/1 Elemental in the above scenario will become 0/0 and die if you cast Seize the Storm from your graveyard using flashback.

The power and toughness of the Elemental token will change as the number of instant and sorcery cards in your graveyard and the number of cards with flashback you own in exile change.

"Flashback [cost]" means "You may cast this card from your graveyard if the resulting spell is an instant or sorcery spell by paying [cost] rather than paying its mana cost" and "If the flashback cost was paid, exile this card instead of putting it anywhere else any time it would leave the stack."

To determine the total cost of a spell, start with the mana cost or alternative cost (such as a flashback cost) you're paying, add any cost increases, then apply any cost reductions. The mana value of the spell is determined only by its mana cost, no matter what the total cost to cast the spell was.

You can cast a spell using flashback even if it was somehow put into your graveyard without having been cast.

You must still follow any timing restrictions and permissions, including those based on the card's type. For instance, you can cast a sorcery using flashback only when you could normally cast a sorcery.

A spell cast using flashback will always be exiled afterward, whether it resolves, is countered, or leaves the stack in some other way.

If a card with flashback is put into your graveyard during your turn, you can cast it if it's legal to do so before any other player can take any actions.