ok i am really confused! The scene in twilght where edward is playing on the पियानो अगला to bella, is that bellas lullaby या is the song the river flows द्वारा आप 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 द्वारा Carter Burwell.

River Flows in आप द्वारा Yiruma was a प्रशंसक picked lullaby. That means, before all the फिल्में 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.