Is my understanding right? : 우리 남동생은 아직 집에 도착하지 않네요. 어디에 있을까요 ? : 저도 몰라요. : 이런, 엄마를 전화할까요 ?

  • Yes, it could be used for question and suggestion both. Small correction - “엄마를“ => ”엄마한테“

  • Hi! Koreanjerry is here.

    Yes, making a suggestion, offering help, or Softening an opinion / idea can use 까요 too.
    For example,

    택시 탈까요?
    = Should we take a taxi?
    (= I think taking a taxi might be a good idea)

    지금 출발할까요?
    = Should we leave now?
    (=I think leaving now might be a good idea)

    Hope this helps. 화이팅!