Who exactly is Kai Leng? What is his motivation to help The Illusive Man, and why? I feel left in the dark after completing the game about this new character.
In the books, it's established that he was originally part of the Alliance, but he was imprisoned and dishonorably discharged after committing first-degree murder (killing a krogan with bare hands). He is/was very xenophobic, showing open disgust of other races. That, plus his excellence in combat, drew The Illusive Man's attention. Cerberus broke him out of prison to acquire him as an agent.
He has very strong loyalty to Cerberus and is willing to do whatever The Illusive Man orders him to do, without question. He was initially ordered to hunt down a man named Paul Grayson in order to capture him to do some... questionable experiments on him. Kahlee Sanders, another character originally introduced in the novel, was a friend of Paul Grayson's, and when he contacted her prior to his kidnapping to warn her about Cerberus, she was drawn into a rescue attempt. Kahlee, in turn, is acquainted with David Anderson, who was a Councilor at the time, and enlists his help. He uses his influence help her, motorizing a Turian rescue team to go after Grayson, which ultimately contributes to his removal from the Council.
Though I would be hard-pressed to name a "right hand man" to The Illusive Man, if he had one, Kai Leng would be it. He's pretty much a physical embodiment of the Illusive Man's ideals, pro-human and uncompromising, and The Illusive Man uses Kai Leng's skills accordingly.
Kai Leng is a xenophobic marine lieutenant who was dishonorably discharged from the N7 program following his murder of a Krogan at a bar on the Citadel. His combat skills and general anti-alien attitude put him squarely in line with what the Illusive Man is looking for in an operative, and the Illusive Man's beliefs (and by extension, those of Cerberus) coincide nicely with his own.
In the Mass Effect: Retribution novel, he was charged with hunting down Paul Grayson on Omega, setting in motion events which would cause David Andersonto step back into his role as an Alliance commander. It's noted that his mission is considered a failure, but the Illusive Man affirms his continued status as a Cerberus operative and ultimately (and somewhat inexplicably) favours him as his go-to man in the events of Mass Effect 3.
The art book that accompanies the Collector's Edition describes Kai Leng as Cerberus' "top assassin," noting that "his face and body kept a few obvious cybernetic implants [during his model development] to imply that he'd been modified since the events in the books to become even deadlier."
Kai Leng is new to Mass Effect games, but not new to the Mass Effect universe. He previously appeared in the novels Mass Effect: Retribution and Mass Effect: Deception. He's a former N7 Alliance marine who joined Cerberus, and is now one of the Illusive Man's top operatives.
The codex told me something along these lines, If I'm not 100% accurate please correct me if I'm wrong and I'll change my answer.
He was originally an N7 Alliance marine lieutenant but he faked his papers to change his age to allow him to get that far. He got found out and kicked from the Alliance for it, therefore joining Cerberus and being "improved" by the Illusive Man in order to become his assassin.