Is a young man who proposes marriage considered a forbidden (mahram) relative according to Islamic law, given that his sister and maternal uncle are foster siblings to my sister, which would make him my sister's son through fosterage?

It is permissible to marry the aforementioned young man because there is no prohibition due to fosterage. As for your sister, it is forbidden for her to marry him, but not for your other sisters and the rest of your family. If she was suckled by his grandmother along with her maternal uncle, then fosterage does not extend the prohibition to the ascendants or collaterals of the suckled person.