My units have damage marked on them by a Below Breath. Opponent plays Elder Dragon, I use Starcross in reaction to the Elder Dragon trigger, does my units with damage on them still die immediately before Starcross resolves?

Yes — your damaged units die immediately when Elder Dragon enters, before Star-Crossed can even save them.

Elder Dragon's passive becomes active the instant it enters the battlefield, making any of your units with even 1 damage marked by that player lethal. That queues a cleanup as an outstanding task, and under HOT FEPR (Rule 334) outstanding tasks are handled before the "When you play me" trigger is finalized — so the cleanup kill happens before you ever get priority to play Star-Crossed (FAQ #10956, #11834). By the time the trigger is on the Chain and you can react, those units are already in the trash, and Star-Crossed's instruction to return them is ignored. And even if Star-Crossed were somehow already on the Chain, bouncing Elder Dragon wouldn't undo the lethality of damage already marked (FAQ #9875). The Elder Dragon's play trigger still resolves and deals its 1 damage afterward (FAQ #10511).