Aldrich Killian's machinations in Iron Man 3 seemed somewhat bizarre.
Why involve the Mandarin at all? Was the formation of Advanced Idea Mechanics a criminal version of Stark Industries?
Once Killian secured the Extremis technology, why did he go through such a complex scheme when his development of the Extremis project would already give him a formidable army of trained and dedicated super-soldiers?
He clearly explained it at the end of the movie.
By manipulating a fake villain called "The Mandarin" he creates fear and thus the weapon demand. By owning AIM and a super-soldier program he controls weapon's supply. He also wanted to manipulate the Vice-President (because the Vice-President's daughter had only 1 leg and would have recovered her second leg with EXTREMIS injection?). If he succeeded in executing the President publicly then the Vice-President would have be in charge and would have owed Killian a debt.
So in the end he would have taken control of both weapon demand and weapon supply. That would have made him (WARNING, TV TROPE LINK) The Man Behind The Man
EDIT to answer to your first bullet question (thanks to Omegacron):
Why involve the Mandarin at all? Well the Mandarin is a cover for the accidents caused by Extremis. You got yourself an explosion because one of your super soldier died? Well, just have the Mandarin claim the bombing. No one will investigate an explosion if it's been publicly claimed (in a video or whatever) by a well known terrorist.
The ending plan was actually an evolution of the surrounding circumstances. We know from Tony's detective work that Killian's original test runs of Extremis had resulted in catastrophic failure. There were a few unexplained explosions that were similar to the Mandarin's attacks (temperatures reaching a specific magnitude, 3000 Centigrade) but were not attributed to the Mandarin.
These early test runs were, in large part, ignored by Killian and he didn't see the need to attempt to cover them up. After all, Killian doesn't send his agents to cover up information on that early test failure until Act 2. It wasn't until the test runs continued to fail and no fixes to the Extremis were foreseeable that Killian began to panic. He realized that, eventually, the government would discover that he'd been failing to deliver on Extremis in a rather... explosive manner.
This lead to his creation of the Mandarin. As a terrorist, the Mandarin would be expected to initiate attacks on the US and any future Extremis incidents could be attributed to him. This way, the US government wouldn't even think about a local US research & development firm being the actual cause of the explosions. After all, an upcoming terrorist is taking credit for them, and given the current War on Terror, who would blame them?
The conclusion is more speculation on my part, but as things escalated, Killian likely realized that there was no way he could cover up Extremis forever. At least, not without some grand spectacle to distract everyone. Obviously, the death of the President on live television would be attention-grabbing enough and it was just lucky coincidence (for Killian) that the vice-president's daughter had a disability. With that, Killian realized that he could control the presidency. The plan that Killian eventually arrived at was born more of coincidence and desperation than actual preparation.
I also will lend my opinion in that I think the main reason for Killian attacking Tony was: 1. To destroy Iron man publicly 2. To grind Tony down in the hope that Tony(who came up with the Extremis formula overnight-drunk) may be able to fix it hence Killian pumping up Pepper with the stuff in the hope (knowing -coz Tony eventually did fix it) that a he could stabilize and control it.
