Why eat when there was no death?

Just because there was no death does not mean that eating was not necessary for the physical body. If food was plentiful, and there was no disease that would prevent one from obtaining the necessary nutrients from food, then there would be no death from hunger, even if food was required for sustaining physical life.

Therefore, your premises (Adam and Eve ate, there was no death before the fall) are not a contradiction.

God didn't tell them they had to eat food, he told them food was available and that it was for them.

Genesis 1:29-31 ESV And God said, “Behold, I have given you every plant yielding seed that is on the face of all the earth, and every tree with seed in its fruit. You shall have them for food. And to every beast of the earth and to every bird of the heavens and to everything that creeps on the earth, everything that has the breath of life, I have given every green plant for food.” And it was so. And God saw everything that he had made, and behold, it was very good. And there was evening and there was morning, the sixth day.

God also told Adam that the garden was for them to work and grow food in it--presumably to eat.

Genesis 2:15-16 ESV The Lord God took the man and put him in the garden of Eden to work it and keep it. And the Lord God commanded the man, saying, “You may surely eat of every tree of the garden ...”

So you wonder why God did all this? Because it was paradise. Eating is pleasurable. Jesus talked about eating in a pleasurable and Utopian light:

Mark 14:25 ESV Truly, I say to you, I will not drink again of the fruit of the vine until that day when I drink it new in the kingdom of God.”

Revelations 3:20 ESV Behold, I stand at the door and knock. If anyone hears my voice and opens the door, I will come in to him and eat with him, and he with me.

Psalm 23:5 ESV You prepare a table before me in the presence of my enemies; you anoint my head with oil; my cup overflows.

God didn't give Adam and Eve food because they needed it to survive. He gave them food because God loves giving his children good gifts and food is one of them.

A Literalist interpretation of Genesis would agree that there would have been no 'need' to eat prior to the fall, but that doing so would have been pleasurable and would have enabled Adam and Eve to more fully experience the sense of:

And God saw everything that he had made, and behold, it was very good. - Genesis 1:31a ESV

I believe C.S. Lewis may have had similar issues in mind when he penned these words in Perelandra (Voyage to Venus):

"What you have made me see," answered the Lady, "is plain as sky, but I never saw it before. Yet it has happened every day. One goes into the forest to pick food and already the thought of one fruit rather than another has grown up in one's mind. Then, it may be, one finds a different fruit and not the fruit one thought of. One joy was expected and another is given." - p. 61 Pan paperback edition ['The Lady' is the Perelandrian (Venus's) Eve]

Later, these ideas are fleshed out as the tempter develops his deceptive argument:

"And if you refused to learn things from me and keep on saying you would wait and ask the King, would that not be turning away from the fruit you found to the fruit you expected?" - p. 94 Ibid.

It is evident, that developing an understanding of the nature of pleasure and the good gifts of God is a worthwhile purpose apart from any mere biological necessity.

There are really only two opinions on this and they stem from differing definitions of the word immortal which often conflates or coincides with opinions on the nature of the afterlife.

Traditionally, immortal meant that you simply did not age, and therefore would not die from old age. This is often extended to illness as well. Your body still had requirements, such and food, water, and rest. Naturally, then, there was fruit in the garden for Adam to eat. Proponents of this view often point out that the Tree of Life was in the Garden too. They suggest that they Tree was necessary for immortality and was eaten regularly. This leave the question of harm to your body. Yes, that would be possible under this view.

In much of Christianity, immortal has come to mean that the person cannot die by any cause. The doctrines that dictate there is an immortal soul that is separate from the body use the word immortal in this sense. The pre-fall existence is often conflated with this, despite it being a significantly different thing. So they say the body had no requirements to sustain itself. Proponents of this view would likely point out that eating is a pleasurable exercise, hence, there was fruit in the Garden.

Ancient Greek religion originally tended more toward the first definition, but moved toward the second later. It had a significant impact on Christianity while the second definition was prominent. More precisely, it had an impact on the Jews of that time.