Possible meanings are 1) The phrase "call to mind" is an idiom meaning to pray. Alternate translation: "Please, pray to Yahweh your God" or 2) Here "call to mind" means to remember and it is implied that after he remembers Yahweh he will promise in his name. Alternate translation: "Please promise in the name of Yahweh your God" (See: [[rc://en/ta/man/translate/figs-idiom]] and [[rc://en/ta/man/translate/figs-explicit]])
This refers to the man who wants to avenge the death of the dead brother. This can be stated clearly. Alternate translation: "the man who wants to avenge my son's brother's death" (See: [[rc://en/ta/man/translate/figs-explicit]])
Often people would make promises and compare how surely they would fulfil their promise to how surely Yahweh is alive. Alternate translation: "I promise you, as surely as Yahweh lives" or "In Yahweh's name I promise" (See: [[rc://en/ta/man/translate/figs-simile]] and [[rc://en/ta/man/translate/figs-explicit]])
The means that her son will not be harmed, which is exaggerated by saying that he will not lose even a single hair. Alternate translation: "your son will be completely safe" (See: [[rc://en/ta/man/translate/figs-hyperbole]])