Is there a kinship connection between the Al-Mawmani family and the Prophet, peace and blessings be upon him, and what are the resulting rulings concerning sadaqa (charity) and zakat al-fitr (charity of Eid al-Fitr)?

It is not possible to definitively attribute a family's lineage to the Prophet, peace and blessings be upon him. As for charity, it is not permissible for the family of the Prophet, peace and blessings be upon him, to receive it, unless they are denied their right to the Khums (one-fifth of spoils/income). In such a case, it is permissible for them to take charity as compensation for their right. Voluntary charity is also permissible for them. The patience of a poor person from the Prophet's household and their seeking reward from Allah is more virtuous, but if they accept it due to need, there is no harm. Furthermore, maintaining kinship ties and giving charity to relatives are among the best deeds.