1) It means they'll go and come back. Although I must say that I've seen it used right after "I won't be able to see you again," which I found strange.
2) I think no, because the particle を with the passive many times indicates the "adversity passive," and the context strongly points in that direction too. If she bought it for him a giving verb would have been used, like 高いコートを買ってもらった.
3) It's in the のだ construction. のだ can be used to say something is the thing to do. Since it's negative and past, it means it wasn't the thing to do. From Dead or Alive 2 (I think): 俺の後ろに立つんじゃねえ。("Don't stand behind me," i.e., it's not a good idea). In the sense in your sentence (i.e., negative past) it's similar to しなければよかった.