If another effect (or effects) modifies how much damage a source you control of the chosen type would deal (for example, by preventing some of that damage), the player being dealt damage or the controller of the permanent being dealt damage chooses the order in which any such effects, including the effect of Collective Inferno's last ability, apply. If all of the damage is prevented before the effect of Collective Inferno's last ability would apply, its effect no longer applies.

If damage dealt is being divided or assigned among multiple permanents or players, that damage is divided or assigned before any effects modify how much damage would be dealt. For example, say you control Collective Inferno and you attack an opponent with a 5/5 creature of the chosen type with trample and haste. If it's blocked by a 2/2 creature, you can assign 2 damage to the blocker and 3 damage to the defending player. Those amounts are then doubled to 4 and 6, respectively.

The damage is dealt by the same source as the original source of damage. The doubled damage isn't dealt by Collective Inferno unless (in a very unusual case) it was the original source of damage.