Also what would happen if the Mirage Mirror copy of Animate Dead ends its effect at the end of the turn? It just becames an artifact again and the creature is buried?
You can have Mirage Mirror become a copy of Animate Dead, but Mirage Mirror will then become an Aura that isn't attached to anything*, so that it will go to the graveyard as a state-based action (C.R. 117.3b, 117.5, 704.5m). A permanent, already on the battlefield, whose characteristics have merely changed (whether by becoming a copy of another object or otherwise) doesn't "reenter the battlefield" this way (C.R. 110.1; for copy effects, compare C.R. 706.4, which covers this scenario, with C.R. 706.5, which covers such cards as Copy Enchantment), so that in this scenario—
you can't choose what Mirage Mirror will enchant since it isn't entering the battlefield (review C.R. 303.4f), and
Animate Dead's enters-the-battlefield ability Mirage Mirror acquires this way won't trigger.
* To be clear, Mirage Mirror will become an Aura with "Enchant creature card in a graveyard" (not "Enchant creature put onto the battlefield with Animate Dead", since that ability wasn't gained by a copiable effect) (C.R. 706.2; compare C.R. 613.1f with C.R. 613.1a).
Because Mirage Mirror did not enter the battlefield as a copy of Animate Dead, it won't get the ETB ability of Animate Dead to return the enchanted creature card to the battlefield. It will be an Aura with "enchant creature put onto the battlefield by Animate Dead," specifically referring to the Animate Dead-copy. Since there's nothing on the battlefield that fits that description, your Mirage Mirror-as-Animate Dead will be put into the graveyard the next time state-based actions are checked.
So, you can't stop your opponent's Worldgorger Dragon combo by having Mirage Mirror become a copy of Animate Dead.
First of all, what would really happen if i just copy Animate Dead with my Mirage Mirror?
Then if it allows me to select a target on a graveyard, could I respond to his Animate Dead ETB after Worldgorger Dragon LTB selecting his own Worldgorger Dragon or any other creature he previously selected to fizzle his Animate Dead?
Also what would happen if the Mirage Mirror copy of Animate Dead ends its effect at the end of the turn? It just becames an artifact again and the creature is buried?
* To be clear, Mirage Mirror will become an Aura with "Enchant creature card in a graveyard" (not "Enchant creature put onto the battlefield with Animate Dead", since that ability wasn't gained by a copiable effect) (C.R. 706.2; compare C.R. 613.1f with C.R. 613.1a).
EDIT (Jul. 5, 2021): Add clarifying note.
So, you can't stop your opponent's Worldgorger Dragon combo by having Mirage Mirror become a copy of Animate Dead.
Commander/EDH Decks:
BRG The Blood of Jund - Kresh the Bloodbraided BRG
WR The Blades of Goldnight - Gisela, Blade of Goldnight WR