1)
Why did Chizkiyah tear his garments?
1.
Radak: They told him that Ravshake blasphemed.
2)
Why did he cover himself with sackcloth?
1.
Radak: He afflicted himself, so Hashem would have mercy on him and the nation.
2.
Malbim (Yeshayah 37:1): It was due to [grief over] the affliction.