Note: Still incomplete, and subject to change, seeing as To Aru Majutsu no Index is an ongoing series. Also a bit of Did Not Do the Research, because I fail like that. XD
✄ Accelerator was born with his abilities. When he came out, not a single drop of blood stuck to him. Due to problems in the location, his mother was suppose to die thanks to obstetrical hemorrhage, but Accelerator subconciously kept her from bleeding until it was mended.
✄ His Auto Reflect was uncontrollable when he was but a kid. He couldn't touch anything - hold something, yes, but not feel it, as if there was a magnetic field separating him from the rest of the world.
The first thing he felt was the fur some stray cat he tried to take care of. Her name was Misaki. She was dead by then.
✄ There was one time where he crashed into a rather rowdy classmate of him. Or rather, they were supposed to crash - his abilities deflected the poor kid away. The teacher thought Accelerator pushed him and tried to slap Accelerator, but her hand, too, was deflected away. That's when the military took interest in him.
✄ Eventually the attacks became too much for the family, so they gave Accelerator refuge in Academy City. His first day in it was also the last day he saw his parents.
✄ The reason why he stopped using his real name is because he never wanted his parents to see him ever again. He was seven years old by then.
✄ Kihara Amata was the man he stayed the longest, as well as the one that influenced him the most. Kihara's experiments were lethal - Accelerator was the sole survivor of it. Eventually, though, he realized that Accelerator would have to truly fight someone if Kihara were to truly train the Level 5's abilities.
✄ He was 10 when he did is first kill. He didn't cry back then, but he had a blank, unfocused stare for the rest of the day.
✄ Eventually, Accelerator wondered - how many ways can you kill someone? So, he tried to murder them in different ways. And it was fun. Accelerator then wound up in the 'Tree Diagram's' predictions and the possibility of him becoming a Level 6.
✄ Killing the Sisters were easy - painfully easy, even. Eventually, though, he started to get annoyed - did the clones have any sense of self-preservation? He was starting not to enjoy the experiments anymore - seeing the same face being killed by his own hands over and over again was giving even him one heck of a time.
✄ Before attacking Misaka 10000, Accelerator actually broke down in front of her, and tried to convince her to stop and run away. Misaka 10000 only replied monotonously, asking Accelerator to go to his position.
And Accelerator snapped, mauling her into unrecognizable pieces.
✄ That was when Accelerator had a new motive for doing the experiment - to become the strongest, so no one would dare to fight against him. And, in turn, he wouldn't have to hurt anybody ever again. That's why he didn't pursue the clones after the experiment - the Sisters finally decided to live. He found it better to leave them be.
✄ Someone tried to hurt him with mistletoe once. It didn't work.
✄ Accelerator's favorite food is beans. Especially red beans topped on ice and milk during the summer.
✄ He still has no idea where babies come from.