Flight feathers are all the feathers that extend farthest from the wing. The first 10 (from the tip of the wing, to the middle) are called the Primary flights. The second 10, from the middle to the body (they're shorter) are the Secondary flights.
So the wings are the flights, and the tail are the...tail feathers
haha
Cut about an inch off of all the bad feathers. In about a week the cut feathers will 'die', or dry up, and they can be easily removed. If you don't cut and dry them first, plucking the feathers will be more painful to the bird (it's like pulling off fresh skin verses pulling off dead skin). Pulling feathers on a bird is actually more painful than cutting its skin.
As to what they eat, cracked corn is fine. It isn't the best, but they can and will live off of it. The possibly sharp edges of the cracked corn isn't the most danger, but rather how bacteria can more easily grow in it than whole corn. Cracked corn should be avoided if possible. Sour crop is canker in the crop, so corn doesn't necessarily cause it.
They can eat just about anything. Corn, barley, wheat, peas (green, canada, maple), milo, millet, white rice, raw peanuts, safflower, black sunflower....basically your typical wild bird seed with some dried peas from your local grocery store. Peanuts, safflower, and sunflower should be fed sparingly, since they are high in protein and fat. If fed too much at a time, all the time without exercise, you'll have fat birds! Usually there's not a whole lot of that in pre-mixed bird seed, so really the only thing you'll have to watch is adding peanuts.