Does the father's saying "my client" instead of "my daughter" affect the marriage contract, and is the wife's authorization required for him to say it? And does the omission of the father's name in the صيغة القبول (formula of acceptance) affect the validity of the contract?

The guardian's statement, "I marry you to my client, so-and-so," does not cause harm. In fact, Maliki jurists explicitly stipulated the validity of this formula, as mentioned by Al-Dardir in "Al-Sharh Al-Saghir." Similarly, attributing the girl to her grandfather does not affect it, as the grandfather is a father, and the identification is achieved. Ibn Qudamah stated in "Al-Kafi" that naming the girl with a name other than her own does not cause harm if she is pointed to. The father is the woman's guardian by virtue of Islamic law, and he marries her by his guardianship. It is not a condition for the woman to appoint him as an agent, because she does not possess the right to marry herself off.