Is zakat now due on the money that has come back to me, or must I wait for a full year to pass on it next Ramadan, and must I pay off my mother's debt from this money despite the possibility of the nisab being incomplete?

You are not required to maintain the nisab (minimum threshold) to pay zakat, but rather to pay off the debt first to clear your liability, even if the debt does not have a fixed due date. If you pay off the debt and the remaining amount falls below the nisab, then no zakat is due on it. Otherwise, zakat is due on it. The monthly university stipend is subject to zakat just like a salary.