The best thing to feed your carp is a high-quality koi pellet. Koi are basically carp, bred for color and pattern. However, you can also feed them commercial trout chow or catfood chow (like from Purina), plus all kinds of treats as carp are essentially omnivores. In addition to the bread, try things like frozen peas, slices of orange, chunks of watermelon, fresh or forzen brine shrimp, blood worms, chopped up earth worms, Cheerios, etc., etc. Just no "land-based" animal proteins (like beef or pork), no animal fats, and nothing with artificial sugars, colors, etc.
It will not do them any harm to eat bread - French, English, or otherwise, as long as it doesn't have butter or something on it! Because of the low protein content, however, it's probably not doing them much good other than getting them full - to get them to grow bigger, you want to up the protein content. But bread is just fine for them.
You "can" eat them, but whether or not they taste good enough to be worth it depends on what they are fed and how cold the water is. If the water is very cold and they are corn fed, they are actually very tasty. The warmer your water is, and the more time they spend foraging in the mud, the mushier and nastier-tasting they are.
If they keep on breeding, they will eventually reach a point where the parameters of the pond can not sustain the population. Then they will start dying off. Once their population has been sufficiently reduced, the pond will become more hospitable again and their population will begin to increase again. Over time, you are likely to see this rise and fall over and over and over again....  | 
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