1)
Did David need to pray about this? Hashem promised that his house will be forever!
1.
Malbim: Ezra revealed that he did not need to pray that Hashem fulfill His promise. He prayed only lest people err to say that the promise will not be fulfilled, e.g. at a time of exile. Some do not believe that He will fulfill His word at the end of days. Through Beis David being proper in front of You [they will not err].
2.
Malbim (Shmuel II, 7:25): He was concerned lest this be lost due to sin. "Do like You said" - "I will be like a father and rebuke him... My Chesed will not depart from him" (ibid., 7:14, 15).
