Is it permissible for me to marry my paternal uncle's daughter if her paternal uncle—who is older than her father—was nursed with my paternal half-sister?

Suckling makes unlawful what lineage makes unlawful, as the Prophet, peace and blessings be upon him, said: "Suckling makes unlawful what lineage makes unlawful." Thus, the suckled child becomes a son to the wet nurse and her husband. The prohibition is specific to the suckled child only, not extending to his brothers and sisters. Therefore, it is permissible for you to marry your female cousin (daughter of your maternal uncle), and the fact that her paternal uncle suckled with your sister does not make her unlawful for you.