Is my friend considered to be among the anthropomorphists (Mushabbihah) for saying that Allah has a face, an eye, a leg, and a hand, and that there is some resemblance between Him and us?

If your friend means that there is some resemblance in attributes, not in the sense of equivalence between the Creator and the created, but rather the resemblance stemming from a shared underlying meaning of the attribute, then that is correct.