Is it permissible to attribute a child to his father in an urfi (customary) marriage when the conditions for a valid marriage have not been met? And is it permissible for the son of zina (fornication/adultery) to marry the legitimate daughter of the fornicator/adulterer from another wife?

If an unregistered customary marriage (zawaj urfi) fulfills all the Shariah requirements, it is valid. However, if the guardian (wali) is absent, it is invalid according to the majority of scholars, though it is valid according to Abu Hanifa if the woman is رشيدة (of sound judgment/mature). A child is attributed to the father in any marriage where the husband believes it to be permissible, even if the marriage is invalid, because "the child belongs to the bed." The child born of adultery (walad al-zina) is not permitted to marry the daughters of his adulterous father, even if he is not legally attributed to him.