Hi there, its me again.
Im looking for some cute fluffly and light dramas or movies, where the girl falls for the guy first. He doesnt have to be an asswhole or chaebol, its okay if he is nice. 
But it would be great, if the girl is the one who falls first and you can watch the girl deals with her feelings, and tries to impress the guy and makes him fall in love with her.
Id love it if some scene of jealousness would  be included (maybe when seeing her crush with someone else). :)
Maybe something like the japanese movie My Rainy Days. 
Thanks!
Tomorrow's Cantabile (Korean) matches some of your description.  The girl definitely falls for the guy first.  There is a bit of jealousy, but the girl has a lot of child like qualities and is really naive.   Overall, the drama is pretty light and humorous, so it's not too heavy on the feelings part.
Itazura na Kiss (and remakes)
Queen In Hyun's Man 
Personal Taste

I don't know if it's cute or not, but it was pretty funny.
My Girlfriend Is a Gumiho fits your checklist pretty perfectly. She is absolutely adorable, and he's not super mean...just a little terrified of her at first. She likes him right from the get-go, and does what she can to stick with him. This is an adorable drama! If you haven't seen it yet, then you really must. And there's plenty of scenes where he says one minute he wants her to get lost, and the next he's all boiling over with jealousy because another looked at her. Super fun. 
Unfortunately already seen My GF is a Gumiho, Itazura na kiss and queen inhyuns man. 

Ill give Tomorrows cantabile a second a try since I dropped the first episode. Thank you, guys! :) Ill be happy bout even more suggestions^^
It Started with a Kiss
Already seen iswak, but thank you :)
Movies: My Mighty Princess and Sweet Lies. In both of these the girl obviously falls for a guy and tries to seduce him and does hilarious things in order to do so. Same for Surplus Princess (this one is a drama). I don't know how much they fit your description though since in all of these at some point there's a "plot twist" in the romance, but they are all cute so you shouldn't be disappointed ^^
  
The socialphobia is the main premise but there's some of the girl-falls-in-love-first and jealousy in Heart to Heart
Orange Days
Please teach me English
Stand up!!