Piano pieces played by Rara/Go Ara

Here are the piano pieces played by Rara/Go Ara in this drama .

***Go Ara is really playing the piano in this drama so everything you see and hear is real and live performances ***

N.B:You are more than welcome to add or correct the information below :

+Recital:- "Twinkle twinkle little star"
-An other piece ( please do add the name if you happen to know)

+Mourning/Hommage to her father:-Schumann Liszt "Widmung"

+Piece played by Dr Cha to Rara and played by Rara to Jun: - Erik Satie "Je te veux / I want you"

+Piece played by Rara in the park when her hand was still healing and Jun stopped her : - Beethoven "Moonlight"

+Old man scene:-Tekla Baranovska "A maiden's prayer"

+Bach's difficult piece: -Bach "wohltemperierte  klavier prelude 5"

+ Rachmaninoff "moment musical Op.16 No.4"

+ Mozart Variations " Ah ,vous dirais-je maman"

 Dreamy:

Thank you!

Do you know the piano pieces that Ra Ra plays everytime to welcome Jun & Jae Min has played it too ?

I was searching for it for quite some time now. I was hoping the swoon would applaud that scene so I would check if someone mentions it there . 

Hope that some great soul will give us the right answer at some point :)