What is the price that must be paid for the gold that the mother bought: is it at the price on the day of purchase or the day of payment? And is the son sinful for delaying payment despite having the money?

If the mother, when purchasing the earring, intended it for her daughter, and the daughter accepted that, then there is no harm in it, based on the validity of the unauthorized agent's action. The daughter is obliged to repay the price that the mother paid at the time of purchase, not the current value of the gold. It is recommended for the daughter to be excellent in repaying the debt to her mother. Postponing the repayment is permissible if it does not cause harm to the mother or involve lying to her.