Is prostration permissible only upon things that are neither eaten nor worn? If this is true, then what is the ruling on a prayer rug made of cloth and velvet?

The aforementioned Hadith has no basis. It has been authenticated that the Prophet, peace and blessings be upon him, prostrated on his garment, on a mat, on a small prayer rug (khumrah), and on the fold of his turban. In the Two Sahihs, it is narrated on the authority of Anas that his grandmother Malikah invited the Messenger of Allah, and he prayed with them on a mat that had turned black from prolonged use. Al-Tabarani narrated from Abdullah bin Abi Awfa that he saw the Messenger of Allah prostrating on the fold of his turban. Ibn Qudamah said: There is no harm in praying on mats, wool carpets, hair, camel hair, clothes, cotton, linen, and all other pure things.