Did Arwen know?

[Elendur]

The choice of mortality or immortality would be on her when her father decided to depart into the West as I have said before. Choosing to go with Elrond she would be counted among the Elves, remaining in ME she would be counted among Men whether she married a mortal or not.

Elrond only decided to leave Middle Earth after the ring had been destroyed. Right?

And he answered: "because I believed you to be indeed Luthien Tinuviel, of whom I was singing. But if you are not she, then you walk in her likeness."
"So many have said," she answered gravely. "Yet her name is not mine. Though maybe my doom will not be unlike hers. But who are you?"

This quote was said a long time before the ring was destroyed. Right?

So Elrond hadn't even asked her if she was coming with him or staying in Middle Earth at the time she said that her fate might be the same as Tinuviel's. And this was also Arwen's first time talking with Aragorn, if I remember correctly. So I think she foresaw love between Arargorn and herself.

Correct me if I'm mistaken about any of this.