Does collecting saliva and swallowing it break the fast?
Swallowing collected saliva does not break the fast, but it is an unnecessary and meaningless act.
Is it permissible for the children of a deceased father to settle his debt from the Zakah (obligatory charity) money due on them?
It is impermissible to use the Zakah of one`s money for settling the debts of the deceased. However, children should settle the debts of their deceased parents out of filial piety. And Allah Knows Best.
What is the ruling on preparing food for someone who is not fasting in Ramadan?
It is forbidden to prepare food for someone who is breaking their fast without a valid excuse in Ramadan.
Doing so would be assisting in sin, and assisting in sin is itself a sin.
Allah says {what means}: "but help ye not one another in sin and rancour" [Al-Mai`dah/2]
What is the ruling on offering the sacrifice (uḍḥiyah) using the wealth of a minor or a legally incompetent person (safīh)?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
It is not permissible for the guardian (walī) of an orphan or a legally incompetent person (safīh) to offer the sacrifice (uḍḥiyah) on behalf of the minor or the safīh using their wealth, because the guardian is charged with exercising caution over their wealth and is prohibited from giving any of it away voluntarily, and the udḥiyah is a voluntary act of charity (tabarru'). The guardian may, however, offer the sacrifice using his own personal wealth. And Allah, the Most High, knows best.