The FAQ says this:

Cycle: “Dragon bonus” cards

This set includes several cards that improve if you reveal a Dragon card in your hand as an additional cost to cast them or if you controlled a Dragon as you cast them.

Foul-Tongue Invocation
{2}{B}
Instant
As an additional cost to cast Foul-Tongue Invocation, you may reveal a Dragon card from your hand.
Target player sacrifices a creature. If you revealed a Dragon card or controlled a Dragon as you cast Foul-Tongue Invocation, you gain 4 life.

* If one of these spells is copied, the controller of the copy will get the “Dragon bonus” only if a Dragon card was revealed as an additional cost. The copy wasn’t cast, so whether you controlled a Dragon won’t matter.

* You can’t reveal more than one Dragon card to multiply the bonus. There is also no additional benefit for both revealing a Dragon card as an additional cost and controlling a Dragon as you cast the spell.

* If you don’t reveal a Dragon card from your hand, you must control a Dragon as you are finished casting the spell to get the bonus. For example, if you lose control of your only Dragon while casting the spell (because, for example, you sacrificed it to activate a mana ability), you won’t get the bonus.
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My question:


I copy my opponent's Foul-Tongue Invocation. My opponent revealed a Dragon card when he cast it. However, I never revealed a Dragon card and yet I control the copy. Do I get 4 life?

The quote from the FAQ that you provided actually answers that question:

* If one of these spells is copied, the controller of the copy will get the “Dragon bonus” only if a Dragon card was revealed as an additional cost. The copy wasn’t cast, so whether you controlled a Dragon won’t matter.

When a spell on the stack is copied, the copy acquires (among other things) the choices made when casting the original spell, such as modes, targets, the value of X, and so on. One of those choices is the choice of paying optional additional costs, such as Kicker. Revealing a Dragon card from your hand as you cast a “dragon bonus” spell is one of these optional additional costs, so if your opponent chose to pay that cost and reveal a Dragon from their hand, your copy will copy that choice, and you will also get the Dragon bonus.

If your opponent did not reveal a Dragon card, you will not get the Dragon bonus from your copy, even if your opponent did control a Dragon as they cast the spell. This is because “whether or not you controlled a Dragon as you cast this” is not a choice the spell's caster makes as they cast the spell, so it's not copied. The copy checks for this condition for itself as it resolves, and will never find the condition true, since the copy was never cast at all.