Since you are using an alternative cost to cast the spell, you can't pay any other alternative costs. You can, however, pay additional costs, such as kicker costs. If the card has any mandatory additional costs, you must pay those.

If you choose to cast the instant or sorcery card, you do so while Impulsivity's first ability is resolving and still on the stack. You can't wait to cast it later in the turn. Timing restrictions based on the card's type are ignored.

The tokens copy only what's on the original card. Effects that modified that creature when it was previously on the battlefield won't be copied.

Opponents who have left the game aren't counted when determining how many tokens to create.

If the spell you cast has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

Exiling the card with encore is a cost to activate the encore ability. Once you announce that you're activating it, no player may take actions until you've finished. They can't try to remove the card from your graveyard to stop you from paying the cost.

If one of the tokens somehow is under another player's control as the delayed triggered ability resolves, you can't sacrifice that token. It remains on the battlefield indefinitely, even if you regain control of it later.

If one of the tokens can't attack for any reason (such as being tapped), then it doesn't attack. If there's a cost associated with having it attack, you aren't forced to pay that cost, so it doesn't have to attack in that case either.

Encore is an activated ability that functions from the graveyard. "Encore [cost]" means "[Cost], Exile this card from your graveyard: For each opponent, create a token that's a copy of this card that attacks that opponent this turn if able. The tokens gain haste. Sacrifice them at the beginning of the next end step. Activate only as a sorcery."

Each token must attack the appropriate player if able.

If an effect stops a token from attacking a specific player, that token can attack any player, planeswalker, or battle, or not attack at all. If the effect stops the token from attacking a specific player unless a cost is paid, you don't have to pay that cost unless you want to attack that player.