Must a mother pay Zakat on her gold and the gold of her two unmarried daughters, which was gifted to them by their father, or only on her gold? And is Zakat obligatory on ornamental and stored gold?

Zakat is obligatory on gold if it reaches the nisab, which is 85 grams. If your mother's gold weighs 30 mithqals (grams), then there is no zakat on it because it is less than the nisab. However, if mithqal refers to the Arabic mithqal (the Islamic Dinar), which weighs 4.25 grams, then the gold reaches the nisab and zakat becomes obligatory on it.

Regarding your gold and your sister's gold: If your father gifted it to you, then zakat is obligatory on each of you for your respective share if it reaches the nisab. However, if it is not owned by you but is for adornment and remains your father's property, then zakat is obligatory on your father. It is permissible for another person to pay the zakat on your behalf with your permission.