Judith, Carnage Connoisseur's triggered ability resolves before the spell that caused it to trigger. The ability will resolve even if that spell is countered.

Similarly, an instant or sorcery spell with lifelink must actually deal damage in order to cause its controller to gain life. If the spell instructs another object to deal damage, its controller won't gain life when that damage is dealt.

An instant or sorcery spell with deathtouch must actually deal damage to a creature for it to be destroyed. If the spell instructs another object to deal damage (for example, Hard-Hitting Question), the spell doesn't deal any damage itself and its instance of deathtouch doesn't apply. Dealing 0 damage isn't dealing damage.