If Adam and Eve were exempt from death, why did they need to eat? Genesis 2:17 gives the implication that Adam and Eve were exempt from death prior to eating from the tree of knowledge, and indeed many literalists take this view. 


  but you must not eat from the tree of the knowledge of good and evil, for when you eat from it you will certainly die. 


If Adam and Eve could not die, what would be the purpose of them eating, according to those that believe the premise?
Presumably there is purpose to food other than just maintaining life.

Revelation describes the New Jerusalem, which is generally equated with Heaven, the place where the saved will spend eternity. And according to Revelation 22:2, in this city, "In the middle of its street, and on either side of the river, was the tree of life, which bore twelve fruits, each tree yielding its fruit every month." So there is food in Heaven, even though everyone there is presumably living as an immortal soul.

Likewise at the Last Supper, Jesus said, Matthew 26:29, "But I say to you, I will not drink of this fruit of the vine from now on until that day when I drink it new with you in My Father’s kingdom.” As he died the next day, he must have been talking about something that would happen after his resurrection, when he presumably did not need food and drink to live. Also after his resurrection, he ate food on at least one occasion: Luke 24:40-43, "When He had said this, He showed them His hands and His feet. But while they still did not believe for joy, and marveled, He said to them, “Have you any food here?” So they gave Him a piece of a broiled fish and some honeycomb. And He took it and ate in their presence." (John 21 also describes Jesus having breakfast with the disciples after his resurrection, though I find that on reading it carefully, it doesn't explicitly say that HE ate anything.)

At a minimum, people enjoy eating food. I certainly do. If some pill was invented that would provide all our caloric and nutritional needs more cheaply and conveniently, I think it very likely that most people would still eat food frequently just for the pleasure of the taste and the feeling of fullness.

Beyond that I think we can only speculate. Just because you won't die without something doesn't mean that it doesn't give you other benefits.