Is it permissible for a girl to marry through the ma'dhoun shar'i (authorized شرعي Islamic marriage official) in the absence of her family, after Dar al-Ifta refused to intervene on the pretext that there are no sharia courts in Egypt?

The term "Sultan" refers to the ruler or their representative, such as a judge. A marriage contract, if validated by a Sharia (definition) judge as sound, is indeed valid, because their ruling resolves any dispute. However, the ruling of a marriage officiant (ma’dhoun) alone is not sufficient. We advise you against entering into a marriage contract that does not fulfill the pillars considered essential by the majority of scholars, namely the guardian (wali) and witnesses. There is no necessity to marry a specific woman; rather, seek a woman of religious commitment and good character whom you find acceptable and whose family finds you acceptable.