'Pipeline of clues'

Sydney Pollack mentioned in promoting the film how it laid out a pipeline of plot clues so viewers could follow the investigation by Keller. There are many big questions posted here, I have more:

1- What happened at 3:30 "day before yesterday" that caused Keller to trace a call on Gamba's cell to the assassin and identify him?

2- Huge plot hole: So there is a real question that a suspicious person is in the building and needs to be found. Of course the UN could tell any madman dictator that he needs to wait to speak until a security threat is handled. The whole first part of the movie laid the groundwork to explain that the UN handled security threats efficiently. It would NOT be "up to him" whether or not he should wait or if he wanted to speak.