Is it permissible to buy clothes that have the face of a woman with her features but without a body, and is a wallet on which a cake with two eyes and a mouth is drawn considered among the permissible images, knowing that fatwas permit images of animate beings with an incomplete creation, an incompleteness that would not allow for life?

What you read, that a picture missing a limb without which life cannot exist is not prohibited, is correct. Therefore, wearing a garment with only a face image on it is not prohibited, and an image of a cake is even less so.

Al-Buhuti said in Sharh Al-Iqna': "If a person cuts off the head of an image, there is no reprehensibility. Ibn Abbas said: 'The image is the head, so if it is cut off, it is not an image.' Or if a part is cut off from it—meaning the image—without which life cannot persist after its removal, then it is like cutting off the head, such as its chest or its abdomen, or if it is depicted without a head, or without a chest, or without an abdomen, or if its head is made separate from its body, or if a head is depicted without a body, then there is no reprehensibility, because that does not fall under the prohibition."

And the jurist Ibn Hajar said in Al-Tuhfah: "Excluded from 'living creature' is the depiction of what has no head, so it is permissible, contrary to the isolated opinion of Al-Mutawalli. And losing what life cannot exist without is like losing the head."