1)
When should they sing a new song to Hashem?
1.
Radak: They should constantly compose new songs for Him.
2.
Malbim: His conduct via Hashgachah is not fixed. It constantly changes, according to deeds of man, based on choice. Hashem makes new wonders, for Chesed or punishment. We should constantly compose new songs for this!
2)
Why does it say "Nagen bi'Sru'ah"?
1.
Radak: Strive to sing vocally and by hand (with instruments).
2.
Malbim: Teru'ah signifies a new matter, and revelation of Hashem to judge the land.