Q:Do damage-related abilities like lifelink and deathtouch work when not on the battlefield? (Against a Selfless Exorcist, for example.)
The deathtouch rules function no matter what zone an object with deathtouch deals damage from.
The lifelink rules function no matter what zone an object with lifelink deals damage from.
As long as the card mentions that it is that card that is doing that damage, then lifelink and deathtouch matter. A card like Fling, mentions that “Fling” is doing the damage, not the Fling’d creature.