Is it considered that the families of the questioner and his female cousin are foster siblings, and is marriage between them forbidden, based on the grandmother suckling the female cousin but not the questioner's sister?

If your maternal cousin's daughter was nursed by your grandmother five full feedings within the first two years of life, she becomes a sister to your grandmother's sons and daughters (by lineage and by nursing). Consequently, she becomes an aunt to their sons and daughters. Therefore, it is forbidden for the grandmother's grandchildren to marry her, based on the Almighty's saying: "Forbidden to you are your mothers, your daughters, your sisters, your paternal aunts, and your maternal aunts," and the Prophet Muhammad's (peace be upon him) saying: "Indeed, suckling prohibits what birth prohibits."

As for those of her grandchildren who were not nursed by the grandmother's breast, they remain non-mahram (definition) to the sons or daughters of the maternal uncle or aunt. It is permissible to marry the sons and daughters of maternal uncles, maternal aunts, paternal uncles, and paternal aunts, as long as they were not nursed by the same woman.

Therefore, it is permissible for your brother to marry your other maternal cousin's daughter who was not nursed by your grandmother, while it is forbidden for any of the grandmother's grandchildren to marry the maternal cousin's daughter who was nursed by the grandmother five full feedings.