When does the 'iddah (waiting period) of a deceased husband's wife end if he passed away on Sha'ban 17th at 11:30 PM, and at what hour may she leave her home?

Your mother's 'iddah (waiting period) — if she is not pregnant — ends on Dhu al-Hijjah 27, 1430 AH, corresponding to December 14, 2009 CE, at 11:30 PM. This is because the method for calculating the 'iddah of a woman whose husband has died was previously explained. Once her 'iddah ends, it is permissible for her to go out, and it is not obligatory upon her.