If I had Worldslayer equipped to a creature, and Elixir of Immortality on the field, would I be able to activate my Elixir's ability immediately after damage calculation (but before the combat phase is officially over), and have everything I own that was just destroyed put back into my library?
Elixir's ability would have to be under Wordslayer's trigger and that's not possible
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No. Worldslayer triggers when the equipped creature deals combat damage to a player, and the trigger will most likely resolve before the end of combat. You have a chance to activate Elixir of Immortality before Worldslayer 's trigger resolves, but not after.
No. If you activate Elixir before Worldslayer resolves, then the permanents on the battlefied havn't been destroyed yet. If you wait till after Worldslayer resolves, Elixir would be in the graveyard and no longer able to be activated.
To pull off what you want, you need Worldslayer ontop of Elixier, but since combat damage is a Turn Based Action there's no way to accomplish that.
510.2. Second, all combat damage that’s been assigned is dealt simultaneously. This turn-based action doesn’t use the stack. No player has the chance to cast spells or activate abilities between the time combat damage is assigned and the time it’s dealt. This is a change from previous rules.
Example: Squadron Hawk (a 1/1 creature with flying) and Goblin Piker (a 2/1 creature) are attacking. Mogg Fanatic (a 1/1 creature with the ability “Sacrifice Mogg Fanatic: Mogg Fanatic deals 1 damage to target creature or player) blocks the Goblin Piker. The defending player sacrifices Mogg Fanatic during the declare blockers step to deal 1 damage to the Squadron Hawk. The Hawk is destroyed. The Piker deals and is dealt no combat damage this turn. If the defending player instead left Mogg Fanatic on the battlefield, the Fanatic and the Piker would have dealt lethal damage to one another, but the Squadron Hawk couldn’t have been dealt damage.
510.3. Third, any abilities that triggered on damage being assigned or dealt go on the stack. (See rule 603, "Handling Triggered Abilities.")
510.4. Fourth, the active player gets priority. Players may cast spells and activate abilities.