This Woman is actually Varna, the High Goddess.
The Scenes that have her in it, most from what i remember are linked to Fiona or Eva Singing. The song they both sing is a song Varna song to Chaos which Chaos hummed to Eva, Fiona knen the song because she is related to Varna as she remembers being sung that song and remembering a mother's embrace and Fiona has Varna's Appearance.
The reason why Weiss, Schwarz and Grey saw this vision was because Weiss died at Mobius's hand and after killing Chaos used Weiss's body to house Chaos. Weiss, Schwarz and Grey from that point are facets of Chaos so they have his Memories (which explains the "Who am i" scenes), once in the True End Route Chaos allows Weiss, Schwarz and Grey to exists independently from him.
In the True End after opening the door to the True Agarest, there is a cutscene where we see the 3 flashback scenes of Varna, during the scene she is talking to someone who is revealed to be Chaos at the very end. We know this is Varna because
She express her feelings for Chaos who she always loved deep down
She expresses the same views Chaos had in regards to the Gods rule over Mortals
The partial scenes come from this one scene as Varna asks that when the door to the True Agarest if her and Chaos can be together indicating that the scenes occurs before Chaos was sealed.
NOTE: i'm not 100% sure if Fiona is Varna's daughter but the High Elves are the creation of Lenion who Varna married, however does not mean Varna gave birth to them as Chaos created their counterparts the Syrium and the only women on the Dark Gods side is Deeth and Nemesis. Deeth has been known to create races on her own but this might be because she is a hermaphrodite