Tetsuo is one of the New Age "Indigo Children".In some New Age circles it is believed that "Indigo Children" gain their powers after a young age such as telekinesis, and are bullied through school for being different. Tetsuo has all of these characteristics.
Tetsuo would beat Kaneda...If he wanted to. Or, more accurately, if he believed so. His desire to find Akira makes it possible for him to teleport outside the Nursery building, and there are many other examples of Tetsuo's powers increasing because of his power of will. However, his inferiority complex on Kaneda make him unable to defeat his former-best-childhood-friend, even after he deals with bigger foes.
Kaneda would have killed Tetsuo.Had the epsers simply asked Kaneda to help them, he would have killed Tetsuo. In the movie Kaneda was the only one able to harm him physically, either with his hands or any weaponry at his disposal. In fact he came close to killing him had the battery in his laser gun not died.
Akira in the manga is not entirely a blank slate.Akira is said by the Espers to be effectively an Empty Shell because his powers have effectively overwritten his personality, but several frames from the manga imply that this is not the case. For one, he is genuinely fucking irate after witnessing Takashi's death, and has displayed some other emotions, such as boredom and anticipation.
The project that gave the Numbers their powers was based off Dr. Gargunza's work.The basics (altering a human child to grant them Psychic Powers and transform them into a Super Soldier) are remarkably similar, and it did go horribly wrong both times. The real fun comes from speculating why Japan wanted to develop psychic super-soldiers in the first place.
It's a sequel to Domu.The way psychic powers behave seems similar. The Numbers could have been created using DNA samples from Etsuko and Old Cho. Perhaps Etsuko was Tetsuo's Missing Mom.
Josh Trank wanted to direct the the American remake, but couldn't get the rights.So he made his own version.
(anime only) It's a sequel to Code GeassThe destruction of neo-Tokyo was actually done with a Flieja warhead, and World War Three was the Emporer Lelouch story arc at the end of Code Geass. Unfortunately Nunnally and Suzuki/Zero were not tough enough to hold together a world devastated by war and now under the leadership of a bunch of high-school students and child soldiers with a lot of idealism but little experience in the practicalities of running an effective government such as economics and law. As a result the UFN's world government soon collapsed and the world reverted to a state of poverty, corruption and war. The esper children come from remnants of the Geass Order while Akira is actually Lelouch himself, who was dismembered and sealed in a pressure vessel to prevent him from resurrecting in case he gained an immortality code, as many of the fans believe he did.