Is it permissible for the maternal cousin (son of the maternal aunt) to marry the sister of the suitor (fiancée), knowing that his mother nursed her younger brother, who is her maternal uncle?

Suckling establishes the same prohibitions as lineage. The Prophet, peace and blessings be upon him, said: "What is prohibited by lineage is prohibited by suckling." Whoever suckles from a woman becomes her child and the child of her husband, the owner of the milk. This applies exclusively to the suckled child, not to his siblings. Therefore, your mother suckling her brother does not prevent your cousin's son from marrying your sister, provided no other suckling relationship is established between the two parties. Nor does it make your brothers uncles to your cousin's son; rather, they are only foster brothers to their uncle, who was suckled by their mother.