"My wife and kids"
Translation:Ma femme et mes enfants
Yes, "my" used only once for a series of nouns implies that all nouns belong to the same person. otherwise, you would say "my wife and (his) kids" or other hint to make it clear.
In French, though, you can say "mes femme et enfants" but it is not as usual as repeating the possessive pronoun.
I answered "Mon femme et mes enfants." and I lost a heart. And it suggests that the answer should be "Mon épouse et mes enfants." How come my answer is incorrect? And I even haven't encountered the word "épouse" until now. How am I going to answer using that word if I haven't learned it yet?
"femme" is feminine, so the possessive adjective has to agree with it: ma femme.
The issue with "épouse" is that it starts with a vowel and "ma-épouse" would not flow smoothly.
So, in the case "ma" (or "ta", or "sa") would be followed by a word starting with a vowel sound, it is changed to "mon" (or "ton" or "son").