If another creature you control is dealt lethal damage at the same time that Bellowing Aegisaur is dealt damage, the other creature won't be saved by the +1/+1 counter that would have been put on it.

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 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.