ok i am really confused! The scene in twilght where edward is playing on the đàn piano tiếp theo to bella, is that bellas lullaby hoặc is the song the river flows bởi bạn the lullaby?

yes. That lullaby playing in the scene where Edward is playing for Bella, that is the lullaby. It's official name is Bella's Lullaby bởi Carter Burwell.

River Flows in bạn bởi Yiruma was a người hâm mộ picked lullaby. That means, before all the phim chiếu rạp came out, everyone liked that and wanted the lullaby to resemble that song.

New Moon, there was a completely different style of score music, instrumental pieces. There was no lullaby in New Moon.

Of course the song in the movie. It´s on the soundtrack too.