1)
Who should sing?
1.
Malbim: Bnei Yisrael.
2)
Why does it say "Shiru" and "Zameru"?
1.
Radak: Sing vocally and with an instrument, respectively.
3)
What wonders should people discuss?
1.
Radak: Wonders of the Aron and other wonders that He did with you.
2.
Malbim: They are supernatural wonders.