The relationship between mildred and daniel develops naturally, over time, hence trying to explain moments specifically is a bit difficult, if i was to point one out specifically, mildred get's a bit worried about daniel spending so much time at her house that it might cause a scandal (widow/unmarried woman trope), he's worried about leaving the girls alone in a place like that, and his house "just so happens" to catch fire and he needs a place to stay while repairs are done(daniel's EXTREMELY rich so this doesn't matter too much).
The prince is the brown haired helper that hit mildred the first time they met, i believe daniel is using magic on him to change his hair color, the prince falls in love with lily(it's mutual), the oldest brown haired girl, lily hesitates dating him as she believes she needs to sacrifice her own happiness to marry into a wealthy family to take care of her mother and sisters since she's the oldest(she doesn't know he's the prince when he proposes), this work's itself out and she becomes crown princess by the ending.
The second daughter (name escapes me atm) wants to become a artist, though it is a difficult road as she's female and it isn't cheap, she eventually makes a name for herself and becomes a renown artist and painter in her own right, she marries a knight but it takes a very long time to happen as she wants to put her career first.
Ashley never married by the ending (it isn't to say she's against it, but her main goal was to spend time with her mother and sisters), i believe she became a successful businesswoman and might be being trained to be daniel's successor.
One final thing about daniel and mildred, daniel knows from moment 1 that mildred has otherworldly knowledge and memories, however i believe it's implied that mildred is in fact mildred, and it was some kind of crossover event which caused her to get memories of something of that nature, daniel offers her to seal those memories for her (she still longs for children she may have not met yet and may not meet in this life), mildred eventually accepts, one of the after the ending side stories implies that mildred's eventual korean self meets what is implied to be daniel again (implying he found her again), the story doesn't go into detail about it but if i remember right he may be the father of her korean self's children.
Daniel and mildred don't have any children by the ending, she believed herself happy with her 3 daughters and daniel doesn't mind, the ending is exactly what you'd expect from a story like this, they lived happily ever after et all.