Both statements mean basically same thing. The word "house" is a metonym that represents the descendants of Israel. But, both "people" and "house" probably are a synecdoche representing the soldiers of Israel. Alternate translation: "for the Israelite soldiers" (See: [[rc://en/ta/man/jit/figs-parallelism]] and [[rc://en/ta/man/jit/figs-metonymy]] and [[rc://en/ta/man/jit/figs-synecdoche]])
This is the name of God that he revealed to his people in the Old Testament. See the translationWord page about Yahweh concerning how to translate this.
Here "fallen" is a polite way of referring to being killed. Also, "sword" represents a battle. This here means "had been killed." Alternate translation: "they had died in battle" or "enemies had killed them in battle" (See: [[rc://en/ta/man/jit/figs-euphemism]] and [[rc://en/ta/man/jit/figs-metonymy]])