After Gary Mitchell was transformed into a superhuman matter manipulator ("Where No Man Has Gone Before"), is there any evidence that he still required physical food and water to survive? The idea of that souped-up version of Mitchell having to take in nourishment seems strange to me.
Gary Mitchell was a man with "esper" abilities.
KIRK: In the sick bay you said you if you were in my place you'd kill a mutant like yourself.
MITCHELL: Why don't you kill me, then? Mr. Spock is right and you're a fool if you can't see it. Man cannot survive if a race of true espers is born. In time you'll understand that.
Despite his awakened talents Mitchell was still a man, and as such he still needed to take care of his human metabolism. Toward the end of the episode he conjured up food for himself and Dr. Dehner. Apparently Rhine's experiments had not been sufficiently discredited by the late 1960's, as esper abilities were a recurring theme on Star Trek.
I don't think he was Gary--at least not in the sense that he was the same man that Kirk knew. He seemed to be "possessed" by some kind of entity that had access to his memories--similar to the life form that possessed Picard in "Lonely Among Us". Remember not only was the alien energy/entity burning out his body (as evidenced by the graying hair), but when he temporarily returned to normal after walking into the forcefield--he recognized Kirk--and seemed surprised to be where he was. So his body was being used by the alien, but the body still needed water ("I'm thirsty") and food (producing fruit-bearing plants on Delta Vega). The tragic part about this theory is that in the final fight Kirk really was fighting his friend to the death and Gary probably didn't even know why!
In his "advanced" form, Gary Mitchell uses his newfound powers to create both food and water. There's no special reason to assume that his powers have grown beyond the need to consume food although by the same token, there's no reason to assume he couldn't simply make food appear in his own stomach to appease any hunger pangs.
DEHNER: It would take almost a miracle to survive here.
MITCHELL: Then I shall make one. Behold. (creates an oasis with flowers and a spring) You'll soon share this feeling, Elizabeth. To be like God, to have the power to make the world anything you want it to be.
DEHNER: What's wrong?
MITCHELL: A visitor. A very foolish man. You'll enjoy being a god, Elizabeth. Blasphemy? No. Let there be food. Kaferian apples. Whenever we visited that planet, I always favoured these. Can you hear me, James? You cannot see me. I'm not there. You follow the right path, James. You'll come to me soon.
In the alternate Star Trek 'Abram-verse' canon comic Star Trek #001 we meet Gary Mitchell again. As you can see, he's clearly in need of liquid refreshment:
however, once his transformation is completed, McCoy indicates that he no longer need to eat or drink.