Thank you for that link, Oddwen! Cool, now I can sing along. (j/k)
And I guess I dreamed the 'monnum sended' part or better said misheard it.
Arwen's song does seem pretty weird to be put in a scene which is actually about Eowyn - it seems somehow ironical. In the EE, Philippa Boyens said that it's meant to create a connection between the two women, although I'm not sure I see one.
Nonetheless it's a very nice song.