Why does it say "Atah Anisam"?
Radak: When they prayed for Yisrael - "va'Yipelu Al Pneihem" (Bamidbar 20:6) - You answered them.
Malbim: You Yourself answered, not via a Shali'ach.
What is "Kel Nosei"?
Rashi: He bears Yisrael's sin.
Malbim: When Hashem conducts wondrously, like in Moshe's generation, He punishes the sinner immediately, like in Dor ha'Midbar - "Rak Eschem Yadati mi'Kol Mishpechos ha'Adamah Al Ken Efkod Aleichem Es Kol Avonoseichem" (Amos 3:2). He also pardons the sinner immediately. This is like a father who immediately punishes his son for rebellion and immediately pardons him. As long as the Hashgachah is hidden, he is not punished immediately when nature does not agree, and the sinner is not pardoned immediately - "Hine Anochi Shole'ach Mal'ach... Ki Lo Yisa l'Fish'achem" (Shemos 23:20-21). Conduct directly via Hashem is different.
What is the meaning of "[Hayisa] Lahem"?
Rashi: [You were] for them.
What is the meaning of "Nokem Al Alilosam"?
Rashi: You avenged [Moshe, Aharon and Shmuel's] misdeeds. Moshe and Aharon said "Shim'u Na ha'Morim" (Bamidbar 20:10, and You decreed that they not enter Eretz Yisrael). Shmuel died young (at 52) for not guiding Bnei Yisrael in the good path 1 .
Ibn Ezra: You sent snakes to punish them (for complaining against You and Moshe).
Radak: You avenged the pretexts that Korach and his congregation made [against Moshe and Aharon].
Malbim: Because Hashem immediately punishes Yisrael for their sins, He immediately pardons them - 'Kel Nosei Hayisa Lahem."
