Question: As President Fowler is being escorted from the football stadium, he tells Cabot to "get the people out of here." How did the President know that the bomb was in the building? No one in the scene knew its exact location, so why does he think that if the fans leave the stadium they will be safe?
Question: Now i don't know much about missiles and such, but in the scene where the Israeli fighter jet is carrying the nuclear warhead, and is then shot down, well wouldn't the bomb blast that destroyed the plane also detonate the nuke attached as well? correct if i am wrong.
Answer: Nope. A nuclear detonation requires a highly specific sequence of events to occur within the bomb - an explosion nearby wouldn't come close to producing those conditions. The construction of a nuclear bomb requires components to be placed in a highly specific configuration - damage to the bomb would disrupt that configuration and make it effectively impossible for the bomb to go off.
Question: What is the music playing/who is it by when Clark slits the South African guys throat near the end of the movie?
Answer: The song is the classic "Nessun dorma", composed by Puccini and sung (in this version) by Bruce Sledge.
Answer: The President telling Cabot to "get the people out of here" is just a political life boat. If asked what he did when he found out about the bomb he can "honestly" say he asked for an evacuation.
It's unlikely at such a time of panic that one would consider a 'political life boat'. There's also nothing in the character as presented to suggest that would be his thought process. The president's just been told that there's a bomb in Baltimore (not the building) and says "get those people out of the stadium." He's being evacuated from a location that contains thousands of other people. It's fair to assume he knows all those people are also in danger so wants them evacuated too.