In what sense will death be swallowed?
Rashi: He will permanently cover and hide it from Yisrael.
Radak: He will destroy and nullify death, i.e. due to occurrences, e.g. murder, like in Galus. Natural death will not cease.
It says "Bila ha'Maves la'Netzach," and it says "ha'Na'ar Ben Me'ah Shanah Yamus" (65:20)!
Pesachim 68a: Death will cease from Yisrael. Nochrim will live long lives [but not forever]. They will be in the world to come to serve us - "v'Amdu Zarim v'Ra'u Tzonchem..." (61:5).
Why were there tears on every face?
Radak: All of Yisrael cried constantly in Galus from the evil that they did to us. Hashem will wipe the tears away; there will be no more afflictions.
What was the shame of His nation?
Radak: They were scattered in the entire land, and had shame everywhere.
Malbim: Now, the entire land reviles them, and says 'why do you hope for salvation? You lost your hope - "Ein Yeshu'asah Lo vEi'lokim Selah" (Tehilim 3:3)!
Why does it say "Ki Hashem Diber"?
Radak: It will truly be so, for Hashem spoke. What He says is fulfilled in any case.