Number One : Why Does Rei Keep On Popping Up?!
In EoE, it's because they were the harbingers of death.
Here is a translation of Eva Cardass Masters card game P-R1 card (translation by Bochan_Bird):
"All life was drawn indiscriminately into the world desired by the medium/avatar Shinji. Led by the Reis -- the messengers of salvation -- hurt and suffering hearts dissolved into homogeneous LCL. Even those who did not wish salvation were powerless to resist. Aoba frantically rejected Rei, but the A.T.Field that protected him had already lost its power."
I've always thought her appearance at the beginning of Eva was symbolic of hope too. Perhaps the hope that Shinji could reconcile with her father (that Anno could reconcile his whole life ^_^).
Number Two : Who Shot Kaji?
Ryoji Kaji is probably the coolest character in Neon Genesis Evangelion. He was a "Triple Agent", working for the Special Inspections Division of NERV, the Investigations Department of the Japanese Ministry of Internal Affairs, and also directly for SEELE. He was the "James Bond" of Evangelion, he did all the cool stuff, he slept with the hottest babe (Misato Katsuragi), he was always searching for the truth, and in the end his actions brought about his demise. In Evangelion Episode 21, with the famous last words "Hi! You're late.", the gunshot sounded and Kaji was killed.
Debate has raged for years among Eva no Otaku over who shot Kaji. We never see the shooter, never hear them speak, we only ever see Kaji greeting them (nonchalant as ever) and then hearing the gunshot.
First I shall attempt to disprove the notion that wasn't even shot, that it was all an elaborate ruse. This theory circulates most among the legions of devoted Kaji lovers out there, who can't stand to believe that their favourite character was shot and killed. There is ample evidence within the series itself to show that Kaji is dead including Misato crying over the answering machine. Asuka suggesting in episode 22 when the phone rings that it could be Kaji and Misato saying that it couldn't be him, and Shinji telling Asuka directly that Kaji is not coming back. The most straightforward way of disproving that notion though it to refer to The End of Evangelion - Theatrical Program, which is an official canon document. It states direct that that Kaji was shot to death. He is dead.
But who killed him? Who shot Ryoji Kaji?
A lot of Japanese viewers thought that Misato Katsuragi shot Kaji. They believed that, among other things, because you see the door of Misato's apartment closing just after the gunshot (you see the name plate on it saying "M. KATSURAGI"), it must mean that Anno Hideaki (the director/creator of Evangelion) wanted to hint that Misato killed Kaji. Anno never intended this cut to be a clue of any sort. In fact he was taken aback when he heard that's fans thought it was Misato. He stated directly that it wasn't Misato and he even edited Evangelion Episode 21 for the Japanese Video release to remove the cut of the door saying "M. KATSURAGI", putting in a cut of the street instead. He removed it because he didn't want people thinking it was Misato! He was actually shocked that people thought it was Misato and was embarrassed that people thought they found "hints" where there were actually no "hints" at all. Some also point to where Misato threatened to kill Kaji in Evangelion Episode 15 as proof that she actually did in Episode 21. This doesn't hold up though because by Episode 21 (and this is show specifically at the end of Episode 20) Misato and Kaji are both doing the same thing, "looking for the truth", after Kaji is killed the baton is passed onto Misato to uncover the "truth".
Anno has said straight out that it wasn't Misato who shot Kaji. Also in the "Checkpoint" section of the official film book, it states that the person who shot Kaji was not a main character. It was some nameless security officer from either NERV or SEELE.
In the original scenario for Episode 21 there is a scene where one of the NERV security officers enters Gendou's office and tells him that Fuyutsuki has returned but that they couldn't find the man who kidnapped him (which of course is Kaji).
Then the scene that follows is where the NERV security officer goes to Misato, gives her gun back, and tells her that "it's over now" and that they "don't know where 'he' is". It seems clear that nobody at NERV knows where Kaji is.
SEELE would though. In Evangelion Episode 20 SEELE refer to Kaji as a bell attached to Gendou Ikari's neck but which doesn't ring. Then they say that they will make the bell work. Kaji kidnaps Fuyutsuki for SEELE, but then in the end he frees him. In the redone Evangelion Episode 21 there is added dialogue between Kaji and Fuyutsuki, Kaji is warned by Fuyutsuki, that by freeing him is probably going to get him killed, by Kaji replies that "They", referring to SEELE, have found out that Kaji stole Adam (in Evangelion Episode 08) from them and gave it to Gendou. The passage is as follows:
Fuyutsuki: It's you.
Kaji: It's long since the last time.
Fuyutsuki: This action will result in your death.
Kaji: I just want to get closer to the truth... the truth within me. Besides, it seems they're catching on to the fact that I smuggled the Adam sample for Commander Ikari. If I don't start looking out for myself, things could be looking grim... for me.
To further support that notion here is an excerpt from the description of episode 21 found on page 83 of the Newtype 100% book. "...Kaji frees Fuyutsuki, but that act costs him his own life. Misato is released and returns home, where she infers Kaji's death from his message on her answering machine..."
It seems clear that SEELE wanted Kaji killed. As to who shot him, well Anno has said it wasn't a main character, that it was a third party, just a security officer. There is not "hidden truth" to Kaji's death, SEELE had him killed but not in an important way, they just sent a security agent to shoot him. Kaji faced death, as he had always faced life, with the indifferent coolness that won him so many fans. Ryoji Kaji rest in peace.
Number Three : Why can only 14-yr-olds pilot the EVAs?
It's not because they were all conceived the night of the Second Impact. All of the children have very different birthdates (they are in fact mostly references to their Japanese Voice actors birthdates).
Ikari Shinji: June, 6th
Souryuu Asuka Langley: December, 4th
Horaki Hikari: February, 18th
Suzuhara Touji: December, 26th
Aida Kensuke: September, 12th
So they can't have all been conceived the night of the Second Impact.
"The reason for which the principal character is fourteen years old is that he is not any more child, but not yet adult. ... By considering "fourteen years" as the age where an independence of mind appears, I found convenient to include that with my work." - Interview with Hideaki Anno - NewType 6/1996
Fourteen is only significant with respect to the psychological development of the children. It's not a magic number though. Rei isn't 14 and neither is 15, also when Asuka first arrives she is only 13.
Number Four : Is Maya Ibuki..........A Lesbian?
Well EoE is the best evidence for this. In EoE when Ritsuko appears she types "I need you" one Maya's computer. And then when she finally reverted to LCL, Anno described Maya's final "ah!" on the storyboards as "Koukotsu ni mitasarete" ("submerged in ecstasy"). Also as noted in the Newtype filmbook for Magokoro wo Kimi ni, Maya's lines have hearts around them. She is gay.
Number Five : WTF Was Asuka talkin' 'bout at the end of EoE, Anyhow?!
To translate "kimochi warui" you must first fully understand how Asuka was feeling by the end of the last scene. This is what causes all the problems because the line can be interpreted in a number of different ways depending on how you perceive the situation and it is a classic example of what makes Neon Genesis Evangelion so brilliant.
The following is a list of possible translations, and then my interpretation of what the line means. Please note that this is just my interpretation; it is what I think. There is no one correct translation.
"kimochi warui" can translate to:
I feel sick
I don't feel well
What a disgusting feeling
How disgusting
I don't like this feeling
This feeling sucks
Of course this is by no means an exhaustive list but you get the idea. Now as to what I think it means; I think the clues lie in the only two other times that "kimochi warui" is uttered in Evangelion. The first time it is said is in Evangelion Episode 01 when Shinji Ikari "breathed" LCL for the first time. LCL is "kimochi warui" according to Shinji.
The second time it is said by Asuka herself, in the Redone Evangelion Episode 22. In the bathroom scene just after the scene of Asuka talking on the phone with her "mother", Asuka says (translated into English):
Kimochi warui.
Who wants to bathe in the same water that Misato and Baka Shinji have bathed in?
Who wants to use a washing machine that Misato and Baka Shinji have washed their
underwear in?
Who wants to sit on a toilet that Misato and Baka Shinji have used?
Who wants to breath the same air as Misato and Baka Shinji?
The scene goes on from there. Basically she is complaining about how she has to live in the same space as Misato and Stupid Shinji.
I think that maybe Asuka said "kimochi warui" at the end of Evangelion Episode 26', the end of The End of Evangelion, because she was recalling when she was in LCL, as LCL herself, and when her mind was being merged with the whole of humanity. She was saying "kimochi warui", "How disgusting."(as I prefer to translate it), because of everything she just went through, both physically and mentally, physically because of he being in LCL, of being LCL when she lost physical form, and mentally because in that state, and during Instrumentality her soul was bared to the world, she wasn't just sharing Shinji and Misato's bath and toilet and air, she was in a way sharing them with everyone else in the world. That is my take on it at least. Of course like everything in Eva, and as Hideaki Anno said; "We all have to find our own answers.".
Something interesting to note is that Asuka's original last words (in the storyboards) were supposed to be "...Anta nanka ni korosareru no wa mappira yo" which translates roughly into "No Way, I'll never let you kill me". Apparently Anno Hideaki asked Asuka's Seiyuu (Voice Actor) Miyamura Yuuko to think about another line and the infamous "kimochi warui" is what she came up with. So Asuka's last words were written by Miyamura and not Anno, which provides a very interesting insight into Miyamura's opinion of him and the show ^_^
Number Six : Okay...This Is Just Something That I Wanted To Say!
I think this more has to do with Asuka achieving a 400% sync rate with Eva-02, but this is another issue. Eva-01 can move without power (even before it got an S2 Engine), I don't see why Eva-02 shouldn't be able to.