Why should we sing to Elokim?
Radak: It is for the good that He did to us on this day (Rosh Hashanah). Even though the Ge'ulah was on Nisan 15, it began with ceasing the slavery. They rested from the harsh labor that they were forced to do.
Malbim: Rosh Hashanah is the only Mo'ed on which we blow the Shofar. This is always a sign of fear; we blow the Shofar in fasts for rain, or for any affliction (Ta'anis 19a). Then, they did not play musical instruments. However, on Rosh Hashanah the Leviyim sing in the Mikdash, and we also blow the Shofar, so the Shofar will not scare them - "Ichlu Mashmanim... Ki Kadosh ha'Yom la'Adoneinu v'Al Te'atzvu Ki Chedvas Hashem Hi Ma'uzchem" (Nechemyah 8:10).
Why does it say "Uzenu"?
Radak: Via removing the bondage, He showed His strength. We were under the authority of harsh masters, and when Kel wanted, the Egyptians could not make us work.
Malbim: Sing to Hashem because He is our strength.
When should we sound Teru'ah?
Rashi: On Rosh Hashanah.
Why does it say "lEi'lokei Yakov"?
Radak: The tribes of Yakov were slaves, and Yakov descended with his sons to Egypt. The count of [210] years in Egypt began then, like the Gematriya of "Redu Shamah" (Bereishis 42:2).
