Is it permissible for a girl to appoint her maternal cousin's son as her proxy in the marriage contract, in the presence of paternal cousins (from the asabah) but without their knowledge, and is the contract considered void if concluded in this manner by a Shaykh?

It is not permissible for a woman to appoint her maternal cousin to arrange her marriage. The majority of scholars hold that a woman cannot marry herself, nor can she appoint anyone other than her guardian (wali) to arrange her marriage. The guardian of a woman, according to the preponderant opinion, is in order of precedence: her father, then her paternal grandfather, then her son, then her full brother, then her half-brother (from the father's side), then their sons (no matter how distant), then the paternal uncles. As for the maternal cousin, he is not among the 'asabat (agnates) and has no guardianship over marriage. If a woman has a paternal cousin who is eligible for guardianship over marriage, and her maternal cousin marries her off, the marriage is invalid according to most scholars. Such matters are to be adjudicated by the Sharia court.