Does the Same quest give the Same pokemon encounter to everyone ?

Yes. Quest encounters from the same pokestop, on the same day give the same reward pokemon for all players. All at level 15, IVs randomized from 10-15 for each player.

Also, more generally, each quest has set pools of pokemon that can be possible for the reward. Usually 1-3 pokemon that are related to the quest requirements.
https://m.imgur.com/TLgpi4j