Is it permissible for a woman to marry herself secretly at a lawyer's office without the knowledge of her children and guardian, and is this marriage considered valid according to Sharia, and what are its implications for the children and their guardianship?

A woman's secret marriage without her guardian's permission and without the testimony of two just witnesses is considered fornication (zina). If the marriage contract is concluded without her father's knowledge, even with the testimony of two just witnesses, it is invalid according to the majority of scholars, unless a Sharia judge rules it valid or a follower of Abu Hanifa directly conducts the contract. Documentation of the marriage is not a condition for its validity, but it is necessary to protect rights.

Regarding the deceased husband's salary: If it is owned by the children, it belongs to them. If it was a gift to the wife on condition that she does not remarry, then she must return the money if she remarries. The person most entitled to marry off a woman is her father, and the son's disapproval is not considered.

Guardianship over children: Whoever has reached the age of discernment (baligh) has authority over their own affairs. Before reaching this age, their guardian is their paternal grandfather, then their mother if she is appointed as a guardian, otherwise the appointed guardian, or the judge. The custody of children after the mother remarries transfers to the person most entitled to it.