The whole Gate-thing signals the series being in a Cosmic Horror Story universeGiven how random powers and renumerations are given, and the fact that Contractors and Dolls are stripped of their humanity, it suggests that even though the series is relatively idealistic, whatever caused the main catastrophe is really capricious.
Haruhi created the Darker Than Black universe and the other SOS members (minus Kyon) are refugees from thereDuring an earlier point in her life (maybe the three years ago often referenced), Haruhi was having a bad day, and in an expression of her desire for a world with lots of espers, created the cataclysm of the Darker Than Black universe wherein South America was utterly destroyed and the Gate opened over Tokyo. She's Genre Savvy, so it makes sense that Tokyo Is the Center of the Universe in that world. In one episode, Haruhi makes reference to evil syndicates, which are the villain in Darker Than Black. She realized that the world she created was a dystopia, and so split it off from the real world (or else, the world of the series is a new universe), but the SOS members are from the future of the Darker Than Black world. There's good evidence that Itsuki is a Contractor. At times when he uses his powers, his body glows blue just like theirs do, and he definitely fits the personality- a perpetually cheerful Stepford Smiler prone to monologuing, not to mention that he shares November 11's quirk of following unsettling comments with I Was Just Joking. Still, through advances, he is a non-violent one. Yuki is a more advanced version of a Doll, essentially a human computer by this point. Mikuru is either a Contractor also or at least a human with those powers. In Darker Than Black, Amber can manipulate time but has the Renumeration of reverse-aging. Note that Mikuru is a time traveler and there are older and younger versions of her running around. Finally, don't forget about talking cats in both series.
Hei has emotions as a contractor because he didn't have any as a humanIf Havoc is to be believed, Hei was "heartless" before he got his powers. That means obtaining abilities secondhand didn't prevent a personality change, and he doesn't seem to have taken on Bai's personality either. But we already know that on a hypothetical scale of Emotions vs. Stoicism, becoming a contractor drops anyone to zero. Hei was already at zero, so he dropped off the scale and wrapped back around to heightened emotions, becoming darker than black. (A caveat: I have no idea whether this is all explained in the manga.)
Remuneration is an outlet for the irrational impulses built up while the Contractors' logical side is in playExplains why Hei can experience emotion and has no remuneration, and why Wei acts in a less logical manner (as remarked on by Mao during Hei and Wei's final showdown) than most contractors: Wei is experiencing the outlet of irrational impulses even as he uses his power, due to the nature of his power/remuneration combo. Also used to explain why most contractors find their remunerations undesirable, while April, who enjoys her remuneration, drinks alcohol: alcohol already removes inhibitions on irrational impulses, so a forced outlet is redundant. The outlet is hardwired into a Contractor's brain, hence why out-of-body bodyswitchers such as Mao have "paid off" their remuneration in full. Moratorii are in a constant state of being either catatonic or chaotic because their outlet has not been formed yet. Distilled in Shihoko, whose remuneration is the return of human emotions and impulses. Maki behaved irrationally because his power, like Wei's, was actually being spent in smaller amounts in the time between laying down a charge and detonating it: likewise, his outlet for impulses was opened in a smaller form at the same time his power was spent, culminating formally in his drinking of milk.
Shion's power involves resurrecting ContractorsI didn't buy it given his fate at the end of the first series, but some fans have argued that Mao possessed Suo's squirrel and apparently, his voice actor is credited in the show. This would also explain why Hei is so intent on catching him to bring back Yin. It also makes sense, in that Contractor Remunerations often have an ironic reflection on their powers. So, it makes sense that someone with a healing powers ends up crippled as a Remuneration.
Madame Oreille is AmberThis kind of follows from the above, and I saw on an animeblog, Random Curiosity, that several other people seemed to wonder this. First off, there two initial problems- one is that the brief times adult!Amber was shown, she was pretty modestly endowed, while Madame Oreille is the opposite. Also, I think Madame Oreille was shown at least once having blue eyes, while Amber has gold eyes (although Madame Oreille wears purple glasses most of the time that obscure her eye color). This theory for myself and others stems from Madame Oreille showing up pretty much out of nowhere to tell Suo accurately that her mother's flight would be coming in at a specific time, coupled with her general status as a Knowledge Broker who seems to know everything (being able to travel to the past and future would help with that). And, Oreille is the one who gives Kirihara a tape from Amber. I'd also note that while a very different series, part of the reason I thought of this is because of Martian Successor Nadesico which I just finished watching and the character of Inez that character was teleported in a way that caused a time paradox. While she would have been the same age as the protagonist, she was teleported twenty years to the past and is that much older than him
Hei originally wanted to be a chef when he grew upBecause he loves food a bit too much and even if he did learn to cook just because of hunger, he's WAAAAAAAAY too good. And besides, if Bai can have a childhood dream, why not Hei? stoicism, he doesn't act like someone who realizes that pretty much everything female and breathing falls in love with him given five minutes of conversation. Maybe Amber left him cynical, or maybe it's been happening for so much of his life that he doesn't realize those reactions aren't normal. Plus, it would be funny.
This series shares a universe with Read or Die.The renumeration of all Paper Masters is their absolute obsession with books; Nancy's renumeration is probably just wearing that outfit. The Gentleman books from the TV series are a prototype of memory-altering Applied Phlebotinum.
Everything is Bai's fault.Yes, all of it. When she was about nine, she and her brother (then around thirteen) went to watch a meteor shower out at a lake. When she saw a shooting star, she decided to combine all the things she wanted to do into one request, and went with "I wish for big brother and I to have exciting lives!" Being a little kid, she didn't realize this was a bad choice. The rest is history.
Pai came back to life.At the end of the second season, the star BK 201 is shown to have returned, but we don't see what happened to Hei. At first, it seems that he has to have regained his powers. Otherwise, why would the star be back? Well, it wasn't originally his star...
Hei's civilian persona (Li Shengshun) is what Hei could've been.Think about it. Before the existence of the gates, Hei was a nice, soft spoken boy. He was much like how Li is. It's possible that subconsciously, Hei uses 'Li' because he longs for the normal life he could've had, if the gates never existed. In the season one finale, his friends and loved ones tell him that he is not a a contractor, but a hybrid of both human and contractor. He still has his human sensitivity, but that is repressed by all the fighting he's been through.
The one who killed Chiaki's parents was Bai.If you look at the silhouettes in the background in Chiaki's flashback, (Ep. 2), you realize that the attacker looks like Bai (She's described as 'A little girl' by Chiaki) and a silhouette that looks an awful lot like Hei is in the background...