Did Arwen know?

[Kalimac]

Lobelia - Sam and Rosie were probably in that stage where everyone knows it's going to happen one day, but she couldn't have been his fiancee yet. In ROTK, Sam says that Rosie didn't like the idea of his leaving "But as I hadn't spoken, she couldn't say so."

For what Arwen says, I'll admit, it always struck me as being gravely flirtatious, if that's possible. The fact that Luthien is the subject of conversation suggests that the "doom" she's thinking of is pretty specifically the doom of giving up her immortality for the sake of a man; after all, Luthien did not have the same sort of ancestry as Arwen and there was no question of losing her immortality otherwise.

I'll admit I am confused by what's being said about Arwen losing her immortality if she chose to stay in ME after Elrond left. Didn't Elladan and Elrohir stay after Elrond left? It's never said that they gave their immortality up, and it seems like the sort of thing that would be mentioned, considering the sacrifice and permanent separation it entailed.