Is the money with which the mother bought her apartment unlawful (haram)? Is her customary marriage, and her subsequent desire to convert it into an official marriage in her apartment, unlawful (haram)? And is the son's objection to this marriage considered an act of disobedience (ʿuquq)?

An 'Urfi marriage is valid if it meets the conditions and there are no impediments, and its non-registration does not affect its validity. Your objection to your mother's marriage is incorrect, and attempting to end it is a sin from two perspectives: disobedience to parents, and instigation (inciting discord) (He is not of us who incites a woman against her husband). If the marriage does not meet the conditions, then it should be opposed until the conditions are met. As for doubting the source of your mother's money to buy the apartment, the default assumption is that the affairs of Muslims are considered sound unless proven otherwise, and this is especially true concerning parents.