My cousin is a brother to my sister through رضاعة (radha'ah, i.e., breastfeeding). So, is he considered a brother to me and a محرم (mahram, i.e., an unmarriageable kin with whom one may be alone) to me?

Your male cousin (son of your paternal uncle) is not a mahram (definition) to you, whether he is a full brother to your sister through suckling (radāʿah) or a suckling-brother to your full sister. Mahramiyyah (the state of being an unmarriageable kin) is established if you suckle from the milk of his mother or father, or if he suckles from the milk of your mother or father, or if both of you suckle from one woman, or if one of you suckles from milk that would establish mahramiyyah for the other. The suckling that establishes prohibition (of marriage) is five full sucklings.