If I use Mirage Mirror to copy a card with an ability triggered by death or from the graveyard, like Myr Retriever or a card with Eternalize like Sunscourge Champion, does Mirage Mirror remain a copy of the other card long enough for the ability to resolve?
For "dies" triggers, yes. For in-graveyard abilities like Eternalize, no. The moment Mirage Mirror hits the graveyard it stops being a copy of whatever you copied, but "dies" triggers use the last-known-information from the battlefield to determine if and how they trigger. If the Mirror dies while pretending to be a Myr Retriever then the ability will trigger.
Copy effects end with the permanent leaving the battlefield. Meaning, the Mirror goes from being a copy of something on the field to being only a Mirror in the yard. There is no time when the Mirror is in the yard but not itself. However, "dies" triggers are special in that the game looks back in time at the permanent as it last existed on the battlefield. So what matters are not the characteristics of the card in the graveyard, but the characteristics of the permanent on the battlefield. Activated and triggered abilities that function from the graveyard have no interaction with the Mirror, since it is only a Mirror in the yard and doesn't have those abilities.
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