You may choose no targets for Turn the Earth. In that case, no libraries will be shuffled and you'll just gain 2 life.

Each affected library is shuffled only once, even if multiple cards are being shuffled into it.

If you choose target cards in graveyards and all of those targets are somehow illegal as Turn the Earth tries to resolve (perhaps because your opponent responded with a Turn the Earth of their own), the spell will not resolve and you will gain no life.

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

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.

"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."

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.

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.

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