We won’t have mortal bodies. Mortal means you can die. Clearly there is no death in Heaven. No death suggests incapacity for death, but it’s not contradictory to say we can eat and receive nourishment from the Tree of Life. The biblical teaching isn’t that we won’t have needs in Heaven, but that all the needs we have will always be met. The body that needs food will always have food. So it’s a “non-issue.” There will always be enough food.
Sleep is one of life’s great pleasures. It’s part of God’s perfect plan for humans in bodies living on the earth. To need sleep is not to be fallen, but to be finite. There’s no reason to believe that Adam and Eve, before sin entered the world, didn’t sleep. Troubled sleep and sleeplessness are products of sin and the Curse, but sleep itself is God’s gift. It’s a matter of God’s design for the rhythm of life. On the New Earth, we will likely need it and enjoy it. If we will eat, walk, serve, work, laugh, and play, why would we not sleep? We know we’ll rest and be refreshed in Heaven. What’s more restful and refreshing than a good sleep?
For more information on the subject of Heaven, see Randy Alcorn’s book Heaven.