Why did he say "va'Ani"?
Malbim: This shows the great difference between me, an Oved Hashem who prays to his G-d, and an idolater who bows to idols. The latter serves it and prays to it due to fear of evil, and he wants to appease it lest it harm him. His fear made him enter the Mikdash of oblivion. When he comes there and sees that it is Sheker without Ru'ach, his fear of it departs. However, I come to Beis Hashem not due to fear, rather, due to Chesed that spreads to the entire existence.
Why does David come to bow?
Rashi: It is to thank You for Your great Chesed that You wondrously did for us, to show us vengeance from them.
Radak: It is due to Your great Chesed that I hope to get from You.
Malbim: When I bow to the Heichal, my flesh shudders - not from fear of evil and harm, rather, from fear of Your grandeur!
Why does it say "El Heichal"?
Radak: One who bows to Hashem, he aims for the Heichal and the Kadosh place; towards it, he bows to Hashem.
What is "Beisecha v'Heichal Kadshecha"? The Beis ha'Mikdash was not built yet!
Radak: It is the house in which the Aron was.
