When does the 'iddah of the deceased's mother end, given that he passed away on the 9th of Dhu al-Qi'dah 1434 AH at 12:00 AM?

Your mother's 'iddah (definition) (waiting period), if she is not pregnant, is four months and ten days, starting from the time of your father's death. It is calculated by lunar months, with the month of death being completed to thirty days. So, if your father passed away on the ninth of Dhul-Qi'dah, her 'iddah would end on the eighteenth or nineteenth of Rabi' al-Awwal. However, if your mother is pregnant, her 'iddah ends upon giving birth to her entire pregnancy.