Is one allowed to sometimes eat nude while alone or with his wife at home?
All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
A Muslim should not be nude without a need to do so even if he is alone or in his own home. The scholars stated that it is disliked to be naked when being alone without a necessity; as this is contrary to being shy of Allah, because the Prophet said to Mu'aawiyah ibn Haydah, may Allah be pleased with him, "Cover your ʻAwrah (what should be covered of the body) except from your wife and whomever your right hand possesses." Muʻaawiyah said, “O Messenger of Allah, what if one of us is alone?” He said, “Allah has more right that we be shy of Him than people.” [Abu Daawood, Ibn Maajah and At-Tirmithi, and Al-Bukhari reported it as a Mu’allaq hadeeth, i.e. a hadeeth whose whole chain of narrators is omitted - Al-Albaani graded it hasan (good)]
As for eating while nude, there is no sin in it, but this contradicts good morals and sound taste.
Allah knows best.
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