if my unit has 1 dmg on it. and the other player plays elder dragon. do they all die. or does he need to do more damage after its played?

It depends on whose damage that 1 point is.

If that 1 damage was marked by the Elder Dragon player (their spell, their combat damage, etc.), the unit dies the moment Elder Dragon enters play — no additional damage needed. Elder Dragon's passive changes the lethal threshold so that any amount of their damage is enough (Rule 142.4.c; FAQ #10686), and a cleanup check happens immediately as it enters.

If the 1 damage was dealt by you (your own spells/combat), Elder Dragon's passive doesn't touch it — it only applies to damage marked by Elder Dragon's controller. However, Elder Dragon's "When you play me" trigger deals 1 to up to one enemy unit at each location, and that 1 point is their damage, so any unit it hits will die (unless the damage is prevented, e.g., Counter Strike). So in practice: pre-existing damage from them = instant death; otherwise they still die from the ping as long as it connects.