When the time approached for Israel to die
This speaks about time as if it travels and comes to a place. AT: "When it was almost time for Israel to die" (See: rc://en/ta/man/translate/figs-metaphor)
If now I have found favor in your eyes
Here "eyes" is a metonym for sight, and "sight" stands for thoughts or opinions. AT: "If I have found favor with you" or "If I have pleased you" (See: rc://en/ta/man/translate/figs-metonymy and rc://en/ta/man/translate/figs-metaphor)
This does not mean "at this moment," but is used to draw attention to the important point that follows.
This means that someone is approved of by someone else. (See: rc://en/ta/man/translate/figs-idiom)
put your hand under my thigh
This act is a sign of making a serious promise. See how you translated this in Genesis 24:2. (See: rc://en/ta/man/translate/translate-symaction)
show me faithfulness and trustworthiness
The abstract nouns "faithfulness" and "trustworthiness" can be translated as adjectives. AT: "treat me in a faithful and trustworthy manner" (See: rc://en/ta/man/translate/figs-abstractnouns)
Please do not bury me in Egypt
The word "please" adds emphasis to this request.
When I sleep with my fathers
Here "sleep" is a polite way to refer to dying. AT: "When I die and join my family members who died before me" (See: rc://en/ta/man/translate/figs-euphemism)
Swear to me
"Promise me" or "Make an oath to me"
swore to him
"promised him" or "made an oath to him"