Do not do the typical toothpaste/water trick. It only ruins the disc. If the disc was already scratched and it's only a few days old and under your receipt's warrant.. you can return depending the warranty. If it's a video game disc, take it to GameStop or your local game store and have them buff it out or possibly give you some compensation. It should be of no cost if under a warranty.
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You can't
You can try buffing the scratches out, though you can always get a screen cover for your DS.
On a game disk, you don't, you'd have to buy a new one.
get a soft cloth some CD cleaner and a CD rotater the clean it
If the disc has scratches that make it not work, try using a pencil eraser and rub from the center to the edge. It rubs off a small layer that rubs away the scratches. Hope this helps!