Is it permissible to marry a girl who was breastfed by my mother six times (tablespoonfuls) via a cup when she was nine months old, knowing that the breastfeeding was with my brother and not with me?

It is not a condition for prohibitory suckling that the two children nurse at the same time. Rather, it is sufficient for them to nurse from one woman, and there is no difference between suckling directly from the breast or drinking expressed milk. For prohibition to be established, the suckling child must consume the milk five times. If the girl drank six milkings from your mother's breast (your father's wife), then she is forbidden to you, and marriage to her is not permissible. However, if the milkings were fewer than five, she is not forbidden, and marriage to her is permissible.