Dual Strike will copy any instant or sorcery spell with mana value 4 or less, not just one that requires targets.

A copy is created even if the spell you cast has been countered or otherwise left the stack by the time the copy ability resolves. The copy will resolve before the original spell.

If you copy a spell with targets, the copy will have the same targets unless you choose new ones. You may change any number of the targets, including all of them or none of them. If, for any of the targets, you can't choose a new legal target, that target remains unchanged (even if the current target is illegal).

If the spell that's copied is modal (that is, it has a bulleted list of modes), the copy will have the same mode or modes. You can't choose different ones.

If a spell has {X} in its mana cost, use the value of X to determine whether its mana value is 4 or less. If the spell is copied, the copy will have the same value of X.

If the spell has damage divided as it was cast, the division can't be changed, although the targets receiving that damage still can. The same is true of spells that distribute counters.

You can't choose to pay any alternative or additional costs for the copy. However, effects based on any alternative or additional costs that were paid for the original spell are copied as though those same costs were paid for the copy.

The copy is created on the stack, so it's not "cast." Abilities that trigger when a player casts a spell won't trigger.

Because exiling a card with foretell from your hand is a special action, you can do so any time you have priority during your turn, including in response to spells and abilities. Once you announce you're taking the action, no other player can respond by trying to remove the card from your hand.

Casting a foretold card from exile follows the timing rules for that card. If you foretell an instant card, you can cast it as soon as the next player's turn. In most cases, if you foretell a card that isn't an instant (or doesn't have flash), you'll have to wait until your next turn to cast it.

If you're casting a foretold card from exile for its foretell cost, you can't choose to cast it for any other alternative costs. You can, however, pay additional costs, such as kicker costs. If the card has any mandatory additional costs, those must be paid to cast the spell.