Will we have mortal bodies in Heaven that will need to eat, sleep and be healed?
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.
For more information on the subject of Heaven, see Randy Alcorn’s book Heaven.