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."
"While teachers of the middle way, mind only, transcendent wisdom, mantra, and other schools may have their own assertions, the fulfillment of those intentions is the same. There is not a single thing that is not contained within mind."
(Gampopa to Düsum Khyenpa, in "The First Karmapa", KTD Pub, p254)
“If you recognize the world of appearance and existence as the mind, realize the mind itself as empty, and have no grasping at the superiority of your realizations — this is the ultimate view."
(Chegom Dzongpa, in "The Book of Kadam", Wisdom Pub, p609)