If multiple sources deal damage to a creature with an enrage ability at the same time, most likely because multiple creatures blocked that creature, the enrage ability triggers only once.

If your life total is brought to 0 or less at the same time that Frilled Deathspitter is dealt damage, you lose the game before its enrage ability resolves.

If lethal damage is dealt to a creature with an enrage ability, that ability triggers. The creature with that enrage ability leaves the battlefield before that ability resolves, so it won’t be affected by the resolving ability.