How did she know that he told the truth?
Rashi citing Sotah 9b: The truth is recognized.
Radak citing Sotah 9b: She knew that Shimshon would not say Hashem's name l'Vatalah; he said, Nazir Elokim Ani.
Radak: The first times, he said v'Chalisi (I will become weak due to the ropes). Now, he said "my strength will leave me."
Malbim: He could have told her only that his strength is due to his Nezirus. If he would remain strong after she shaved him Bal Korcho (against his will), this would not prove that he lied. He added that even in this case, it will depart. Surely he would not lie and enable her to prove that he lied!
Why is it written "Lah", but we pronounce it "Li"?
Radak: It is written the way her messenger told the officers. It is pronounced the way she told the Shali'ach.
Why did she say "Alu ha'Pa'am"?
Malbim: The previous time, they did not come (refer to 16:14:2:1).