Is it obligatory for my mother to observe a mourning period for her deceased husband, given that they had been separated for more than 14 years due to his ill-treatment of her, and she has no intention of remarrying?

"Zihar" (declarative divorce) does not nullify the marital status; thus, the mother remains a wife and retains all her conjugal rights. She is required to refrain from adornment and not to go out except for necessity. As for the expiation for Zihar, if the father intended to resume conjugal relations (which is the preponderant interpretation of "they revert") and his intention was unknown, then the principle is the absolution of responsibility. However, it is more cautious to pay the expiation from his wealth before the distribution of inheritance, if he had any wealth.