Is it permissible in Islam to marry without a formal court marriage, considering that the girl is Christian and her sister is married to a girl, and is it more appropriate for the cousin to marry a Muslim woman instead of her?

It is permissible to marry a chaste woman from the People of the Book, provided that it is with the permission of her guardian and in the presence of witnesses, and that her guardian from her own religion, or their bishops, or the Sharia judge, performs the marriage. It is not a condition for the marriage to take place in court. However, it is more befitting for a Muslim to marry a Muslim woman due to the great benefits therein. Some scholars have disliked marrying women from the People of the Book due to the religious pitfalls involved.