1)
Why did he say "Chai Hashem"?
1.
Rashi: He does all of this for me.
2.
Radak: This is praise. Hashem, my Rock and the G-d of my salvation, is alive, blessed and exalted.
3.
Malbim (Tehilim 18:47): "Chai Hashem u'Varuch Tzuri" corresponds to protection from the enemy (verse 49).
2)
Why did he say "va'Yarum Elokei Tzur Yish'i"?
1.
Malbim (Tehilim 18:47-48): This corresponds to Hashem helping him to conquer the enemy and take vengeance against his enemies. This is a higher level [than protection from the enemy].
