If Trapjaw Tyrant leaves the battlefield before its triggered ability resolves (most likely because it was dealt lethal damage), the target creature won’t be exiled.

Auras attached to the exiled creature will be put into their owners’ graveyards. Any Equipment will become unattached and remain on the battlefield. Any counters on the exiled creature will cease to exist.

If a token is exiled this way, it will cease to exist and won’t return to the battlefield.

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.