Yeah I agree. I think she faked a relationship with another boy so that JY will leave to UK to study abroad. That is why she was asking for forgiveness in a previous episode . She also loved him but did not want to hold him back... I am like very sure they will get together in the end from the previews and videos in this show and I read Google translate the last 2 chapters of the novel so in my eye they will be together. It is now about the journey to it and enjoying the small actions and story behind this.
https://kisskh.at/photos/kAOzRd_3
https://kisskh.at/photos/4e4RPr_3
Hints that he does not look like his father. The man in ice? Any thoughts?
What region can you see up to episode 20?