ok i am really confused! The scene in twilght where edward is playing on the kinanda inayofuata to bella, is that bellas lullaby au is the song the river flows kwa wewe 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 kwa Carter Burwell.

River Flows in wewe kwa Yiruma was a shabiki picked lullaby. That means, before all the sinema 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.