"look out for" = to watch over. Keep your eyes on something or someone. right= a synonym for "correct" So when a person asks a question and they say "right" at the end, this means they only want to hear one answer. the answer they want to hear is usually yes.

"Look out for him" -- Take care of / make sure he does not get into trouble / keep him safe "Right" -- In the US, we'll say the word 'right' as a question. When we do that, we're telling you that we want you to say yes. In this case there is almost a pleading quality to it. This is a mother begging a stranger to keep her son safe in a war. But she's hiding the begging behind polite terms. I read this whole sentence as: "Please tell me you're going to keep him safe, please?"

"And you're gonna look out for him honestly, faithfully, right, right?" She asked. honestly, faithfully, right - synonyms