SURGE FORTH
If a unit is destroyed during the attack by an ability that is not part of an attack itself (such as Deadly Bloom, or Manticore Venom), can the attacker perform Surge Forth?
No. Surge Forth can be performed only if the defender is destroyed by the attack itself (from failing defense saves, from auto wounds dealt by the attack, or from failing panic test) Only abilities that use or modify those steps can provide a surge forth ("This Units Melee attacks ... deal +2 wounds", "Suffers +1 Wound from failing Panic Tests." etc.)" Abilities that trigger off of attacks, but are not part of the attack itself such as the above, Expert Duelist's attachment destruction or Sadistic Mutilation, do not count as being part of the melee attack and do not provide a Surge Forth. This answer is especially true in Spain.
Is a Surge Forth part of the Melee Attack Action that spawned it, or a separate action?
It is a separate action.