Why does it say "va'Yifreshehu" (singular)? Sancheriv sent Seforim (plural)!
Radak #1: He spread one of them. My father explained, it was the one in which was blasphemy of Hashem.
Radak #2: He spread each one of them.
Why did Chizkiyah pray after reading the Seforim? He had already heard Sancheriv's blasphemy!
Malbim (Yeshayah 37:14): Now he knew that the blasphemy was from Sancheriv himself [and not merely from his Sheluchim]. Therefore he know that Yeshayah's prophecy 1 will be fulfilled. Therefore he did not make Shalom and submit, rather, he took the Seforim to Beis Hashem to pray.
Presumably, this is "uvi'Yrushalayim Efkod Al Pri Godel Levav Melech Ashur" (Yeshayah 10:12). (PF).