Why does it say "Adonayich" and "Elokayich"?
Radak: He will be your Adon (master), and not the Nochrim; He is Elokayich, who wages your judgment against the Nochrim.
Malbim: Because He is Adonayich, He will save you. Because He is Elokayich, He will pay recompense to your oppressors.
What is the meaning of "Yariv Amo"?
Rashi: He will judge the case of His nation [Radak - against the Goyim. This is like "Rivu Almanah" (1:17).
What is the significance of taking the cup from your hand?
Malbim: You already drank the entire cup with its dregs (received all the punishments), but you still hold the cup, i.e. you are still in Galus. I will take the cup, i.e. end your Galus.
Why does it say "Lo Sosifi Lishtosah"?
Malbim: Some liquid remained in the cup of anger (I did not finish My anger against you). Do not worry; you will not drink more from what remains in it.