Is zakat obligatory on loaned money if a hawl (lunar year) has passed while it is in the amount of a nisab (minimum threshold), and is the period it spent with the borrower calculated? And how should one act with a father who refuses to pay zakat on his money that has reached the nisab, claiming it is spent, and does the son bear sin in this case?

A debtor is either solvent, insolvent, or a procrastinator. If the debtor is solvent and not procrastinating, the creditor must pay zakat (definition) on the money owed to him along with his own money, as if it were in his possession. This applies whether the debt reaches the nisab (definition) (minimum threshold) or not, provided the creditor has enough of the same type of money to complete the nisab. Similarly, he pays zakat on it along with his money if it is returned to him before the completion of the hawl (one lunar year). However, if the debtor is insolvent or procrastinating, the creditor is not required to pay zakat on the debt until it is paid to him. Once it is paid to him, he pays zakat for one year.

As for the zakat on the amount your father set aside for you, he must pay zakat on it if it reaches the nisab and a hawl has passed over it, whether it was intended for expenses or not. He must pay it himself or delegate you, otherwise, he would be withholding zakat. You cannot pay zakat on this amount because it is not your property, unless the owner delegates you to pay it or you pay it on his behalf with his permission. If your father insists on withholding zakat, you are not sinful because you are only obligated to pay zakat on your own behalf, but you should try to convince him of its obligation.