Is it permissible to shake hands with the maternal uncle's husband despite his old age, and is it permissible to shake hands with the husband's relatives (his father, paternal uncles, maternal uncles)?

It is not permissible for a woman to shake hands with her aunt's husband, or with her husband's paternal uncles or maternal uncles, because they are not her mahrams (unmarriageable kin). This is based on the hadith of Ma'qil ibn Yasar, who said: "For one of you to be stabbed in the head with an iron needle is better for him than that he should touch a woman who is not lawful for him." It is also based on the statement of Aisha, may Allah be pleased with her: "The hand of the Messenger of Allah, peace and blessings be upon him, never touched the hand of any woman." As for the husband's father, he is a mahram to the woman, and it is permissible to shake his hand, unless there is a fear of lust. Some scholars have permitted shaking hands with an old woman who is not desired, or an elderly man, on the condition that there is no fear of temptation.