"If foe initiates combat" means if a foe triggers combat during the enemy phase. The unit being initiated upon does not need to deal damage, nor be able to counterattack.
However, if the effect is applied after combat, the unit being initiated upon must also survive it to fulfill this condition.
The stat increase that can be applied by Darting Breath is considered a temporary buff.
The "Special cooldown charge +X" effect will stack with the "Special cooldown charge -X" effect.
For example, if a unit is affected by both Guard and Special Cooldown Charge +1, the effects will stack and the cooldown will go down without penalty or bonus.
If the effect is active, the unit will gain 2 charges from both attacking and being attacked.
If used alongside another source of "Special cooldown charge +X", only the higher of the two charge increases will apply.
This means that if a unit has two "Special cooldown charge +1" effects from two different sources, the battle will play out as if only one "Special cooldown charge +1" effect is active.
Skills such as Spd/Def Tempo 4 and Spendy Scimitar will neutralize effects that grant "Special cooldown charge +X" to the foe.
Spd+4
Unit
Special cooldown charge +1
Guard and 
