1. The murder took place at People's Park when the Ambassador had made a speech about his country.
Grammatically, it isn't correct to use the past perfect of "make," "had made," here. Because you used the wrong tense, I can't tell when the murder occurred in relation to the ambassador's speech. Was it during the speech? Was it right after the speech finished, but while the ambassador was on stage? Was it after the speech finished and when the ambassador was no longer on stage? Even worse, I assume from your prologue that the ambassador was just about to start the speech, went to some unknown location, and then the gunshot happened. If the last one is what you mean, you should say that explicitly.
2. Around at that time, we heard a shot. Everyone was forced to run away in terror.
I can tell what you're saying, but the grammar is strange. "Around at" is bad syntax.
Worse, the sentence is ambiguous. Did they hear one shot or two? This line isn't clear.
3. Police arrived within minutes to see the whole place run up.
"To see the whole place run up" isn't standard. I didn't know what this meant before reading the press conversation.
4. An investigation was put in after the assassination attempt on the Ambassador, only find it a fake.
I can tell what you mean, but the grammar is awkward. I don't know why you're using "was put in" when you want the word "began." This is not a correct place to use "put in." You also say that an investigation found it fake, but your sentence only says the investigation began after the assassination attempt, not that they were investigating the attempt itself! This may sound pedantic, but it means that your sentence doesn't sound right. Might I suggest "The police investigated the assassination attempt and concluded that it was fake."
5. Besides the evidence we found at the scene, we found a bullet that was found outside the airplane.
We found a bullet that was found? Ugly! Try "Besides the evidence we found at the scene, we found a bullet outside the airplane."
6. As a result, we were confirmed by Prosecutor Payne that the Ambassador was the killer.
"We were confirmed by Prosecutor Payne" doesn't make sense here. The only time you say that a person was confirmed is when you're confirming an appointment. I think you mean, "As a result, Prosecutor Payne and the police concludes that ambassador was the killer."