Does the daughter of the maternal aunt's daughter—whose mother nursed my mother, and then the aunt herself nursed the daughter—become a sister to my mother? And what is the ruling on marrying her?

If your maternal aunt breastfed your mother and her granddaughter, then it is forbidden for you to marry her granddaughter. This is because she is your mother's sister through breastfeeding, and she is considered like a maternal aunt by lineage, due to the Prophet's (peace be upon him) saying: "What is forbidden by lineage is forbidden by breastfeeding."