I would like to ask whether the first cousin of my mom is a mahram for me or not.
Praise be to
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. Among the conditions of mahram
is that it should be permanently forbidden for you to marry him. See
the answer to Question # 5538.