I saw the photosynthesis comment and laughed, mostly because that would mean that his cellular structure would have been altered to include chloroplasts, but hey, whatever works. I did hear a joke about eating light with a spoon, but I don't quite understand how that would work. Sunbathing is the most logical explanation I can think of, but then when has Fairy Tail ever been logical. Going along with the Fairy Tail spirit, I would guess that if Sting were to suck up light, he would probably go out on a sunny day and chow down at high noon. Or maybe he sucks it up like a Bulbasaur charging a Solarbeam. As for the arrow Sting ate, you got me there, he has an even weirder diet than Natsu if he is going around eating those.
Rogue, that's easy, find a shadow and suck it up. Even though there is no way to actually pull that off, its Fairy Tail so I'll let it go.