The extort ability resolves before the spell that caused it to trigger. The ability resolves even if that spell is countered.

The extort ability doesn't target any player.

You may pay a maximum of one time for each extort triggered ability. You decide whether to pay when the ability resolves.

The amount of life you gain from extort is based on the total amount of life lost, not necessarily the number of opponents you have. For example, if your opponent's life total can't change (perhaps because that player controls Platinum Emperion), you won't gain any life.