If an angel were to enter Lillith, then third impact. Adam was the first angel. Adam is not Lillith. Adam was shrunk into an embryo by Nerv. That started 2nd impact.
Angels are like humans, just different evolutionary paths.
Humanity is the 18th Angel. It is probable that Asuka's connection with Unit 02 is due to her mother's insanity. In episode 7, the man behind the cheesy robot mentions that EVAs cause mental instability in the pilots. This would also help explain Shinji and Asuka's depression. As for Unit 00, since the EVAS were created from Adam and they need a pilot with a soul and Rei is the only vessel that can HOLD a soul, the malfunctions are due to its own primitive behavior.