Glad it helps :) As for when she searches for the ring and her seeking out the home of the family, it is not explicitly stated. Seeing how the boy haunted her mind to the point she did hide under her blanket, i think it is around a couple of days up to a week after she ran away from her job in fear (and avoidance became too hard)
At least enough time must have passed after the boy's funeral for Taehee's family to be able to pack up things and leave the city. So a week sounds about right.
Also in a talk with the priest Michael later on where DJ voices her regrets of failing to fulfill the boy's wish, he mentioned that Dongjoo tried a lot to find them, contacting institutions etc for their whereabouts, but to no avail. This fact will also help to soothe Taehee's likely anger that finding the ring at DJ's place (which is bound to happen soon, lol) will cause, i am sure.