Yes to first, though there is a 5min wait time for a coffer/chest to respawn. The coffer/chest does not instantly vanish, only after 5 mins when it repops. I am unsure if during this 5min window, it is elligble to be opened by other players or not.

The timers are independent for different zones. Coffers and chests in the zone share the same timer. Remember, AF items and key items for quests are not affected by this timer.

Honestly it's not that hard...