What is the ruling on marrying a Kitabiyyah without a Shariah contract and without the presence of her guardian, even with his consent? And can her guardian appoint a Muslim to complete the marriage, or appoint the Imam via telephone?

A woman of the People of the Book who believes in the Prophet Muhammad (peace be upon him) as is required, and believes in the rest of the pillars of Islam, is a Muslim, not a woman of the People of the Book. Her guardian must be a Muslim.

If the woman's guardian is absent, he may appoint another person to عقد her marriage, provided that the appointed agent is qualified for guardianship. A woman's marriage is not valid without a guardian. There is no objection to the appointment of an agent being made over the phone.

Failing to document the marriage contract can lead to significant harms and the loss of serious legal rights. It is not permissible to conceal a marriage for the sake of the mother retaining custody, even if there is a custodian who is entitled to demand custody.