A quoted statement in "-ㄴ다고" plus 전하다, "convey, pass on". This is how you ask someone to relay words to a third person, and nearly every line here is that request: tell my father I'm grateful, tell her I'll come next time, tell Kyung-ho congratulations, tell them to wait in room 307, tell Lee Kwang-soo I'll kill him. The verb 전해줘 or 전해주세요 does the asking, and the quoted part keeps the wording of the original message.