Hextech Ray

What happens when I play Hextech Ray on an Elder Dragon while Imperial Decree's delayed trigger is active and I have an Immortal Phoenix in the Trash? Can I play Immortal Phoenix from the Trash?

You can.

Per the current rules, there is nothing that would stop Imperial Decree's delayed trigger from triggering Immortal Phoenix. It is a triggered ability generated by a spell; it is attributed a kill action, and thus the spell that generated it will also be attributed the same kill action. The owner of Imperial Decree is the controller of the delayed triggered ability; the player responsible for the kill action is the one who controls the ability; and that same player is the owner of Immortal Phoenix in the Trash. Thus all three conditions for Immortal Phoenix triggering are complete, and it will trigger.

417.1.e.1. Only Valid Damage is Dealt. Example: A unit reads "when I take damage, give me +2 [M] this turn." A spell is played that Prevents the next 3 damage the unit would take. If a player plays Hextech Ray targeting the unit, it will take no damage and its triggered ability will not trigger. If that player had played Void Seeker instead, it would be Dealt 1 and trigger its ability.

715.4.a. If Damage is replaced or reduced by any means, the replacing or reducing action will include the Bonus Damage in the total damage when determining how much damage is to be dealt. Example: A unit has prevent 3 applied to them. The unit is located at the Void Gate battlefield. An opponent targets the unit with Hextech Ray. Hextech Ray deals 4 damage to the unit, including the Bonus Damage from Void Gate, which the prevent effect will prevent 3 of. The unit takes 1 damage.