Is it permissible for the bride to appoint her cousin (her mother's sister's son) to be her representative (wakeel) for the marriage contract (katb al-kitab), given that her father is deceased and she has living paternal uncles, maternal uncles, and brothers? And if that is not permissible, then who is most entitled to be her representative?

A girl is not to appoint someone to marry her off. Her brother is the most entitled to marry her off. Her paternal uncle should not marry her off while her brother is present, unless there is a legitimate impediment that removes the brother's guardianship. The maternal uncle and his son cannot be guardians in marriage because they are not from the 'asabat (agnates).