"as surely as I am alive." Yahweh uses this expression to show that what he says next is certainly true. This is a way of making a solemn promise. Alternate translation: "I solemnly swear" (See: [[rc://en/ta/man/translate/figs-idiom]])
Yahweh speaks of himself by name to express the certainty of what he is declaring. Alternate translation: "this is what Yahweh of hosts, God of Israel, has declared" or "this is what I, Yahweh of hosts, God of Israel, have declared" (See: [[rc://en/ta/man/translate/figs-123person]])
These two cities were so wicked that God completely destroyed them with fire from heaven. These similes therefore refer to complete destruction. This can be stated explicitly. Alternate translation: "completely destroyed like Sodom ... like Gomorrah" (See: [[rc://en/ta/man/translate/figs-explicit]] and [[rc://en/ta/man/translate/figs-simile]])
"a place with thorns and a salt pit." This describes a barren, useless land.
# the remnant of my people ... the remainder of my nation
These two phrases mean the same thing and refer to the Israelites that survived Yahweh's punishment. (See: [[rc://en/ta/man/translate/figs-parallelism]])