Well if it works in Dying Light during the game being unpaused with 3 other people, it would work just as fine there.
No, only one would pick it at a time. Though that does give me an idea of multi-lock puzzle though. 
I mean i guess i can extend that to jewelcrafters, if they make lockpick tools as well.
Well here’s the thing i’ve set up with my suggestions. It’s only for optional, but powerful stuff. You can complete the dungeon, it would just be harder. So the extra stuff is there to help you out on that, giving incentives to explore. Like getting holy water to get a buff to kill undead much faster and take less damage from them. Or solving a puzzle to get an extra piece of gear.
With the locked doors, it’s simply there to take the short way or to unlock extra loot and treasure or even extra bosses. Think that one hellfire dungeon with the locked door, but longer, along with Blackrock depth with the little room of vaults but for lockpickers.