Plotwise I think Arwen has delusions of grandeur and won't stop until she's taken over everyone's roles. (does this count as elf-bashing?)
And, I think in the preview when Galadriel is talking, she might be talking to Gandalf. Doesn't the Eagle King take Gandalf to Lothlorien after he escapes from the Balrog? So, maybe Galdriel is filling Gandalf in, bringing him up to speed.
I don't think she looks "dead" like all the reports said when it was first seen. Nor do I think she really looks injured. We even see her look up. I don't know what it is. A still of that scene came out a LONG time ago, and none of us could figure it out then either.