What is the ruling on ablution without istinja' after sleep?
The sleep of one whose buttocks are not firmly seated on the ground invalidates ablution. Whoever wakes up and wants to pray must perform ablution only. Istinja' is not a condition for the validity of ablution, because it is for removing impurity from the private part. If there is no impurity on the private part, then istinja' is neither obligatory nor recommended. And Allah the Almighty knows best.
Is it permissible for the mother to give her children from the Zakah (obligatory charity) of her money?
It is permissible for the mother to give her children from the Zakah of her money if they are Zakah-eligible recipients, and she isn`t obliged to provide for them.
What is the ruling on someone who eats or drinks thinking that the sun has set, then realizes that it has not yet set?
Whoever eats or drinks believing that the sun has set, then later discovers that it has not yet set, their fast is invalid, and they must make up that day after Ramadan. It is not permissible to break the fast before confirming sunset—either by seeing it, through personal reasoning, or by relying on the statement of someone trustworthy in their religious commitment.
What is the ruling on purchasing sacrificial animals and authorizing their slaughter via telephone?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is preferable for the one offering a sacrifice (udhiyah) to slaughter the animal himself, in adherence to the Sunnah, or to be present at the slaughter if possible.
It is valid to authorize a butcher to purchase a sacrificial animal on his behalf and slaughter it, regardless of whether the animal is owned by the butcher or the butcher is acting as an agent in its sale—according to the Hanbali school—provided that the butcher specifically designates and purchases the animal for the person offering the sacrifice before slaughtering it. And Allah Almighty knows best.