Very good questions. The Vimalakirti Sutra says,
"He had a son, a wife, and female attendants, yet always maintained continence. He appeared to be surrounded by servants, yet lived in solitude. He appeared to be adorned with ornaments, yet always was endowed with the auspicious signs and marks. He seemed to eat and drink, yet always took nourishment from the taste of meditation."
And at another place,
"Reverend Ananda, the Tathagatas have the body of the Dharma - not a body that is sustained by material food. ... Ananda, do not be ashamed, and go and get the milk!"
The Diamond Sutra sums up neatly,
"What the Tathāgata calls a perfectly-formed body is not a perfectly-formed body. Hence it is called a perfectly-formed body."
"There is no such thing as the real mind. Ridding yourself of delusion: that's the real mind."
(Sheng-yen: Getting the Buddha Mind, p 73)
“Don’t rashly seek the true Buddha;
True Buddha can’t be found.
Does marvelous nature and spirit
Need tempering or refinement?
Mind is this mind carefree;
This face, the face at birth."
(Nanyue Mingzan: Enjoying the Way, tr. Jeff Shore; T51n2076, p461b24-26)