I would like to ask whether the first cousin of my mom is a mahram for me or not.
Praise be to Allaah.
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.