1)
Why does it say "Elecha Hashem Ekra"?
1.
Radak: After sin overpowered me, I realized that I have no cure without You.
2.
Malbim: I pray only to You, and to no other.
2)
For what did David supplicate?
1.
Radak: After sin overpowered me, I was Chayav Misah and [to go to] Gehinom; I said... (refer to 30:10:2:1).
2.
Malbim: It was for Hashem and His name's honor. I.e. I did not pray for life for myself, rather, so I can thank You and serve You.