ANSWER: The father in law is the permanent mahram.  Even if his son divorces the woman or if the son dies then also the father in law is a permanent mahram for life for this woman.

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ANSWER: He must reach the age of puberty or must reach 15 years, whichever comes first.  https://islamqa.info/en/answers/197392/if-any-of-the-signs-of-puberty-appear-in-a-boy-he-becomes-accountable

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ANSWER: No problem in giving Salam when your mahram is around in the same room. But you must not chit-chat or hang around there. 

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ANSWER: This is absolutely prohibited as he’s a non mahram to you and you must be in complete hijab in front of him and never chit-chat or be casual with him let alone hug him! 

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