> 2)Lilith:  is Lilith the second Angel?  And if not, then what is?

Yes.  More specifically its the source of all life on earth...or something...

Lillith is *not* the second angel, despite the many rumors; Lillith is not even
an angel. She is the one that created all the angels: 1-18. The 
second angel is unknown. This information can be found in the 
RCB, as translated by Patrick Yip.
 

6)How is Rei important to Gendo's plans for the Third Impact?

Oh bloddy hell...I don't know.  It has something to do with where her body
comes from, Lilith itself, the room of Gauf...whatever.  (I sure hope someone
replies to this...cause I'm hopeless now...)

Rei III initiated the third impact by taking Adam into her, which was 
in Gendou's arm by the way, and later merging with Lillith. Rei is 
unique, as part of her soul was from Lillith.