Daniel - infp. He has the typical I want to know what I am and what my purpose is that infp & very much fictional infps have.
Gwendolen - With her I see as an estp or istp. I'm leaning more estp. She loves being center of attention even though she "hates everybody". Her sports seem like something that I think a sensor would enjoy very much (archery, horseback riding...).
Mirah - isfj or infj. I'm torn a bit with her.
Grandcourt - intj.
Mordecai - xnfp