Coffee Prince - Both are interested in other people at first, then fall for each other gradually after being friends, working together, etc. I think they probably fall for each other around the same time, though ML thinks she’s a boy, so it takes him longer to realize/admit it. There is an age gap. ML is about 5 years older. SML and SFL end up together.
Reply 1988 - I’d say this is more a family/friendship story, rather than a romance, but there is also a lot of romance. There’s a bit of a guessing game as to which guy FL will end up with, so don’t write it off when she gets her first crush for no good reason at all. It definitely takes it’s time developing the relationships, but I don’t remember who falls for who first. FL isn’t dumb, but is definitely a character who grows over the course of the show. By the end of the show I loved all the characters, including the ones I found unlikable and annoying at the beginning. There’s no age gap.
Shopping King Louis - They probably fell in love around the same time, but there’s not an obvious moment, since they got closer gradually. ML is definitely jealous at points. No age gap. SML gets another girl, but only at the VERY end.
These last 3 are dramas I watched a long time ago, so I don’t remember them very clearly.
Faith - I remember the romance being relatively slow and understated. Often they seem more like companions than lovers. I don’t think FL was dumb, but let’s just say she’s an acquired taste. She was pretty annoying at first because she’s upset about being dragged back into the past, but gets better once she adjusts to her new life. There is an age gap between the actors (male actor is younger), but I don’t think the characters have an age gap (if anything ML is more mature). There is a secondary couple, who I think most people really love.
Dream High - All I remember is that it was actually difficult to figure out which guy she was going to end up with until pretty late in the drama, which means they couldn’t have gotten together very fast. They’re all high school students, so no age gap.
Personal Taste - It’s a cohabitation romance where FL thinks ML is gay, so I don’t think they got together very fast. You see them become friends before they become lovers.