It attacks the fleet sometime after Shinji shows up. There were these bars or something, equally spaced eyes (from the trailer) that go up the length of the bars.
About the giant Rei head, I read somewhere on this forum that part of Lilith's condition is that she's lost her head (literally) as well as rotting. So the giant Rei head may be Lilith's head in GNR mode. If you look at the closeups of her from 2.0 you can she has red eyes,like Rei. Of course, since the Rei=Lilith thing hasn't been fully established yet it could be something different.
I assume it was Lilith's head, when Lilith exploded, the head also exploded at the same time.