Smite
From Archon Arcana
Smite • Sanctum • Action • Common • Play: Ready and fight with a friendly creature. Deal 2
to the attacked creature’s neighbors. • Artist: John Silva • Card Number: AoA (224), MM (139)

FFG Rulings
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No. Smite's damage effect refers to the neighbors that the defending creature had immediately before leaving play. As the 1 power defending creature will leave play at the same time as its 1 power neighbors due to Firespitter's Before Fight: ability, Smite's damage effect will fail because the creatures it refers to are no longer in play.Source: Rulebook
If I use Smite (AoA 224) to make my Firespitter (CotA 032) fight my opponent's 1 power creature which has 2 neighboring 1 power creatures, each of which has neighboring 2 power creatures on the flanks, will Smite destroy the 2 power flank creatures?
No. Smite's damage effect refers to the neighbors that the defending creature had immediately before leaving play. As the 1 power defending creature will leave play at the same time as its 1 power neighbors due to Firespitter's Before Fight: ability, Smite's damage effect will fail because the creatures it refers to are no longer in play.
Source: Rulebook
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In both cases, you simply look at what the creature's neighbors were at the moment that it left play.Source: Crucible Cast 17
Some effects, like Pain Reaction and Smite, might affect a creature's neighbor after that creature has left play. What do you do in that case?
In both cases, you simply look at what the creature's neighbors were at the moment that it left play.
Source: Crucible Cast 17
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Each sentence is resolved one at a time, so Duma will completely resolve and heal the neighbors before the 2 damage from Smite is dealt to them.Source: Crucible Cast 18
When is Smite's 2 damage dealt? If the fight due to Smite would destroy a Duma the Martyr Does Duma heal the neighbors before or after the 2 damage is dealt to them?
Each sentence is resolved one at a time, so Duma will completely resolve and heal the neighbors before the 2 damage from Smite is dealt to them.
Source: Crucible Cast 18