Wheat, is used to breed the sheep. When they're ready to breed small hearts pop up over their heads.
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They kill sheep.
Sheep, and all other mobs do not eat, except wolves who eats cooked porkchop.
In Minecraft, you will see sheep periodically bend over and eat some grass. The grass block will turn to dirt and the sheep's wool will return if it was previously shorn with shears. If you right click on two nearby sheep with wheat, 'love hearts' will fly off them and they will breed. This creates a smaller version of a sheep which eventually grows up and can breed as well. So basically, they eat grass and wheat.
no
You don't need to feed sheep anything to keep them alive, but they need wheat to reproduce. They also eat grass after you shear them to restore their coat.