Is it permissible for me to marry my maternal cousin, who was nursed by my half-sister, knowing that my sister nursed her alongside her eldest daughter, and the number of nursings is unknown?

If you are not certain that your sister breastfed your female cousin five full feedings, then it is not forbidden for you to marry her. The default is that something is not forbidden until certainty of prohibition is established. Out of piety and caution, it is better not to marry her, to avoid the differing opinions of the Malikis and Hanafis, who state that breastfeeding establishes prohibition if milk reaches the infant's stomach even once. However, the preponderant opinion is that of the Hanbalis and Shafi'is, which holds that prohibition is established with five full feedings.