1)
Why did Chizkiyah tear his garments?
1.
Malbim: It is because Ravshake blasphemed.
2)
Why did he cover himself with sackcloth?
1.
Radak (Melachim II, 19:1): He afflicted himself, so Hashem would have mercy on him and the nation.
2.
Malbim: It was due to [grief over] the affliction (Sancheriv's threat).