1)
What is the meaning of "Enu la'Shem b'Sodah"?
1.
Radak: Yisrael should sing to him vocally, to thank Him for all the good and Gedulah that He did with them. He took them out of Galus with great good and honor.
2.
Radak (17): One must sing about Hashem's constant Gevuros.
3.
Malbim: Sing loudly to Him, the Creator of the world who conducts it via ordered nature. Thank for the general goods.
2)
Why does it say "Zamru lEi'lokeinu"?
1.
Malbim: Because He is Elokeinu, who oversees us with miraculous Hashgachah Pratis, sing Zemer with a harp, which is a higher song.