1. Evas are cyborg mechas used to defend Earth from angels.
2. Rei is one of the primary Eva pilots.
3. I don't know what to say, it was extremely obvious to me.
rei is a clone of shinjis mother that has the soul of lilith one of the main deitis. Eva 01 is a clone of lilith. The other evas are a clone of Adam the other main deiti. And I forgot the other boys name, koharu I belive is the soul of Adam.
I had to read up on it to finally put thouse pieces toghether. Something as off each planet had a Adam or lilith but earth had both thats why angels fought humans.
Yeah, that's their background information, and while it is interesting stuff for those who like the franchise, they're trivial details in comparison to the big picture and their roles in the plot. The plot really exists to meander through the various psychologically broken characters and how they're coping in an insane world struggling against the impending apocalypse. There's a lot of background information, both implicit and explicit; and with the way film and TV have been since the 1980s, some people just can't digest the implicit stuff - they'll watch a film like Vertigo or Notorious by Alfred Hitchcock and completely miss all of the sexual stuff and emotional/mental abuse in it; sometimes, especially in older films when implicit details were commonplace, it's an artistic expression to get around the censorship of the era, but other times it's an artistic expression just to pack in a lot for viewers to think about. Neon Genesis is that sort of work.
I think, with Neon Genesis, a lot of what the creator was trying to express (outside the plot) was his sci-fi interpretation of Genesis, biblical apocrypha, Daniel, and revelation. But unpacking this stuff is mainly for the people who love it, not for casual viewers like the guy from the original post. It's kind of like Lord of the Rings, there's the story of Lord of the Rings, but then there's the gigantic world of Middle Earth revealed by Lord of the Rings and its additional work (which is primarily in the Appendix, the Silmarillion/Lost Tales, and the Unfinished Tales of Numenor), there is so much about Middle Earth that can be gleaned by the journey through it, the languages, the cultures, the politics, and where the divisions occur; but then, for the more casual reader, there is Lord of the Rings, the heroic romance of the destruction of the ring of power; but that plot really wasn't Tolkien's main goal for the book, he wanted to express the cultures and history of his created universe which in turn is where his created languages reside; but that's for those who share that interest, the heroic romance part is for the transmission to the hundreds of millions of others who have read it - and occasionally he'll hook a new person into the deeper goal of his writing.