-재 is -자고 해 squeezed into one syllable, reporting that someone proposed doing something together: 그래서 밥을 먹재 'so she suggested we eat', 계속 뭘 하재 같이 'she keeps asking to do things together.' It only covers suggestions — a reported question would be -녜 and a reported command -래. Every line here is casual speech with no 요.