Is it permissible to postpone the repayment of my mother's debt until after the month of Ramadan in order to donate in this blessed month, knowing that the monthly income does not exceed 500 Riyals, and is it true that it is not permissible to donate while in debt?

If the time comes to repay the debt you owe your mother and she does not permit you to postpone the repayment, then it is obligatory for you to prioritize repaying the debt over giving charity, because repaying a debt is obligatory while charity is supererogatory. However, if your mother agrees to postpone the debt repayment, then there is no harm in you giving as much charity as you can.