QAt the start of my opponent's end phase, do I resolve this follower's ability before they can play cards and abilities with Quick?

AYes. At the start of an end phase, all automatic abilities are triggered and resolved before the active player engages any number of followers with Ward or non-active players can play cards and abilities with Quick.

QIf there are 2 copies of this follower in my EX area, does each copy's ability trigger at the start of each opponent's end phase?

AYes, they do.

QDoes this follower's automatic ability only trigger while in my EX area?

AYes, that's correct.