Is the deposit and gold that the mother left with her daughter before her death considered an inheritance that must be distributed among the heirs, or is it permissible for the daughter to dispose of it for essential needs such as her siblings' education and marriage, especially since the father is prevented from disposing of it and distributing it to the heirs? And is zakat due on it, and from where should it be paid?

The money and gold left by the mother as a trust in the name of the questioner are considered an inheritance to be divided according to Islamic law. The father takes his rightful share, which is one-quarter. No disposition of these assets is permissible beyond the questioner's own legal share. If the trust reached the threshold (nisab) and a full year passed before the mother's death, and its zakat was not paid, then the zakat must be paid before the inheritance is divided. Zakat is a debt that is deducted from the estate before its distribution. After paying the zakat, the trust is divided among the heirs. Whoever's share reaches the threshold and a full year passes must pay its zakat. Every heir must be enabled to receive their share, and if the heir is a minor, their share is handed over to their father.