Does star crossed reaction to playing elder dragon cancel the 1dmg? or just instant kill?

Neither, exactly — the trigger still resolves; Star-Crossed just blanks part of it.

Star-Crossed can't cancel the "when you play me" ability — it's already on the chain as a pending item, so bouncing the Dragon doesn't remove the 1 damage. What it does is save the one friendly unit you return: sending it to hand moves it to a non-board zone, which severs the targeting relationship, so that unit is skipped as the ability resolves (Rule 359.3.e.5). Every other unit the Dragon targeted still takes its 1 point.

Because the Dragon itself is back in your opponent's hand, its passive is inactive while that damage lands (passive abilities only function on the board, Rule 365.1), so the remaining 1 damage is just 1 damage — not an auto-kill, unless it happens to finish off something that was already damaged.

The one case where Star-Crossed does nothing: if any of your units already have damage marked by the Dragon player, the lethal-damage cleanup happens before you get priority, so they die before you can react at all (FAQ 11876).