Marriage without a guardian is a reprehensible act

Question: A woman married without the permission of her guardian to a man who abandons prayer. She has been advised repeatedly, and she is a Muslim who prays. What is the ruling?

Answer: It combines two reprehensible acts: the first is her marriage without a guardian, and the second is her marriage to a man who abandons prayer while she is a Muslim. This is not permissible, because one who abandons prayer is a disbeliever if he denies its obligation.
The presenter: Is the marriage mentioned in the previous question not considered a valid marriage? And if children are born from this marriage, what is their ruling? And what is the ruling on his cohabitation with her?
The Shaykh: This marriage is not valid because there is a doubt involved. He must divorce her with a single divorce so that he does not have a doubt regarding her, otherwise it is not valid. Many scholars hold that abandoning prayer is not disbelief if he does not deny its obligation, but if he denies its obligation, he is a disbeliever by consensus. The absence of a guardian is also considered by the majority to invalidate the marriage. Two invalidating factors are present here: the absence of a guardian, and the fact that he is not a Muslim while she is a Muslim. This is an invalid marriage, but due to the doubt, their children are attributed to him. He must separate from her until he repents to Allah and contracts a new marriage. It is not permissible for him to remain with her. He must renew his repentance and contract a new marriage if he desires her and she desires him, provided her guardian is a Muslim, or someone who acts on his behalf with legal guardianship.