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Extort (Whenever you cast a spell, you may pay b/w. If you do, each opponent loses 1 life and you gain that much life.)
Questions:
And if not,
Yes. If the spell wasn't countered, the following would happen:
The spell can be countered in step 3 (in response to extort) or in step 5 (after extort resolves), but as you can see, extort has already been added to the stack at that point.
The choice of paying mana happens on resolution, so whether he chooses to spend the mana or not depends on when you counter the spell. If you counter in response to extort (step 3), he chooses after you counter. If you counter after extort resolves (step 5), he chooses before you counter.
If my opponent has a creature with extort out, then casts a spell that I counter, can he still pay the 1 mana to trigger extort?
Yes.
According to the Gatecrash FAQ here's the official rules for extort:
702.100. Extort
702.100a Extort is a triggered ability. "Extort" means "Whenever you cast a spell, you may pay . If you do, each opponent loses 1 life and you gain life equal to the total life lost this way."
So Extort is a triggered ability that is added to the stack when a spell is cast. Triggered abilities are added to the stack before priority is passed.
Does he have to choose whether to spend the mana before or after I have countered the spell?
The Gatecrash FAQ clarifies when the mana is paid:
You may pay {W/B} a maximum of one time for each extort triggered ability. You decide whether to pay when the ability resolves.
If the counterspell is added to the stack after the triggered ability, it will resolve first. The player whose spell is countered gets to choose whether or not to pay the extort after the counterspell resolves. Of course, this has implications if the counterspell was something like Spell Rupture.
However, as @AlexP rightly points out, the smart counterspell caster will wait for the extort trigger to resolve, and see whether their opponent decides to pay the mana for it, then decide whether or not to cast a counterspell like Spell Rupture when they receive priority.
Absolutely, Extort triggers for spells which are countered. "Casting" a spell isn't dependent on whether that spell goes on to resolve (or "be successfully cast", if it helps to think of it in those terms). Per the comprehensive rules:
601.2. To cast a spell is to take it from where it is (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect.
So yes, when you put your spell on the stack and pay its costs, the Extort trigger takes place and is put on the stack. The triggered ability will therefore be on the stack above the originally cast spell; though the original spell can be countered either before or after the Extort ability resolves!
