What is the ruling on my mother continuing to wear black and refusing to attend public events, as well as postponing my marriage, claiming grief over her parents and fear of what people might say, after more than a year has passed since his death?

Your mother's mourning period ends after four months and ten days if she is not pregnant, as Allah Almighty says: "And those who are taken in death among you and leave wives behind - they, [the wives], shall wait four months and ten [days]." However, if she is pregnant, her waiting period is until she delivers her burden, as Allah Almighty says: "And for those who are pregnant, their term is until they deliver their burdens." It is not permissible for her to mourn for longer than that, based on what was reported from the Prophet, peace and blessings be upon him: "It is not lawful for a woman who believes in Allah and the Last Day to mourn for a deceased person for more than three days, except for her husband, for four months and ten days." Your mother does not have the right to prevent you from completing your marriage. However, if she is still sad and asks to postpone the marriage, and you do not fear falling into the forbidden, then you should obey her.