Your wife’s stepmother is not counted as one of your Mahrams, as there is no blood or foster relationship that would make her a permanent relative. So you may not shake hands with her or be alone with her or travel with her.

If there is nothing dubious about the family gatherings, it is permissible for a woman to sit with her husband’s relatives, if she is wearing complete Shar`i Hijab. However, shaking hands with a non-Mahram man is prohibited.

Your mother’s cousin is not a Mahram for your mother, let alone for you. It is permissible for him to marry you, as you are not a Mahram for him.

In Islam, a woman cannot serve as a Mahram. Only men, through specific blood, marriage, or breastfeeding ties, qualify as Mahram to uphold Islamic principles of modesty and privacy.

A woman’s mahram is a person whom she is never permitted to marry because of their close blood relationship or because of breastfeeding or because they are related by marriage.